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test/3_yukicoder/1600_2.test.cpp
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- Last update: 2026-09-15 08:25:53+09:00
- Problem: https://yukicoder.me/problems/no/1600
Depends on
alg/monoid/dummy.hpp
- alg/monoid/min.hpp
- ds/bit_vector.hpp
- ds/dummy_data_structure.hpp
- ds/hashmap.hpp
- ds/index_compression.hpp
- ds/sparse_table/disjoint_sparse_table.hpp
- ds/sparse_table/sparse_table.hpp
- ds/static_range_product.hpp
- ds/unionfind/unionfind.hpp
- ds/wavelet_matrix/wavelet_matrix.hpp
- ds/wavelet_matrix/wavelet_matrix_2d_range.hpp
- graph/base.hpp
- graph/tree.hpp
- mod/modint.hpp
- mod/modint_common.hpp
- my_template.hpp
- other/bit.hpp
- other/io.hpp
Code
#define PROBLEM "https://yukicoder.me/problems/no/1600"
#include "my_template.hpp"
#include "other/io.hpp"
#include "ds/wavelet_matrix/wavelet_matrix_2d_range.hpp"
#include "ds/static_range_product.hpp"
#include "alg/monoid/min.hpp"
#include "graph/tree.hpp"
#include "ds/unionfind/unionfind.hpp"
#include "mod/modint.hpp"
using mint = modint107;
void solve() {
LL(N, M);
Graph<mint, 0> G(N);
UnionFind uf(N);
vc<pair<int, int>> edges;
vc<bool> in_G(M);
mint wt = 1;
FOR(i, M) {
LL(a, b);
--a, --b;
edges.eb(a, b);
wt += wt;
if (uf.merge(a, b)) {
in_G[i] = 1;
G.add(a, b, wt);
}
}
G.build();
Tree<decltype(G)> tree(G);
auto& par = tree.parent;
vc<int> X, Y, W;
FOR(e, M) {
if (in_G[e]) continue;
auto [a, b] = edges[e];
a = tree.LID[a], b = tree.LID[b];
if (a > b) swap(a, b);
X.eb(a), Y.eb(b), W.eb(e);
}
using Mono = Monoid_Min<int>;
using ST = Sparse_Table<Mono>;
Wavelet_Matrix_2D_Range<int, false, false, Static_Range_Product<Mono, ST>>
seg(len(X),
[&](int i) -> tuple<int, int, int> { return {X[i], Y[i], W[i]}; });
LL(Q);
FOR(Q) {
LL(u, v, idx);
--u, --v, --idx;
auto [x, y] = edges[idx];
if (par[y] == x) swap(x, y);
bool in_u = tree.in_subtree(u, x);
bool in_v = tree.in_subtree(v, x);
if (!in_G[idx] || in_u == in_v) {
print(tree.dist_weighted(u, v));
continue;
}
// 木の外に出る移動が必要
int l = tree.LID[x], r = tree.RID[x];
int min_i = Mono::op(seg.prod(0, l, l, r), seg.prod(l, r, r, N));
if (min_i == Mono::id()) {
print(-1);
continue;
}
auto [p, q] = edges[min_i];
bool in_p = tree.in_subtree(p, x);
if (!in_u) swap(u, v);
if (!in_p) swap(p, q);
mint ANS = tree.dist_weighted(u, p) + tree.dist_weighted(v, q);
ANS += mint(2).pow(min_i + 1);
print(ANS);
}
}
signed main() {
solve();
return 0;
}#line 1 "test/3_yukicoder/1600_2.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1600"
#line 1 "my_template.hpp"
#if defined(USE_PCH)
#include <my_template_compiled.hpp>
#else
#if defined(__GNUC__)
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
// 環境によってはコンパイル成功かつ実行時エラー
#pragma GCC target("avx2,popcnt")
#endif
#include <bits/stdc++.h>
#include <cassert>
using namespace std;
using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class>
constexpr bool dependent_false = false;
template <class T>
constexpr T infty = [] {
static_assert(dependent_false<T>, "infty<T> is not defined");
return T{};
}();
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<i128>;
template <>
constexpr long double infty<long double> = infty<i128>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using pq_max = priority_queue<T>;
template <class T>
using pq_min = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR1_R(a) for (ll i = ll(a) - 1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = ll(a) - 1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = ll(b) - 1; i >= ll(a); --i)
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload3(__VA_ARGS__, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define all(x) (x).begin(), (x).end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
// require y > 0
template <typename T>
T floor(T x, T y) {
return x / y - (x % y < 0);
}
// require y > 0
template <typename T>
T ceil(T x, T y) {
return (x / y) + (x % y > 0);
}
// require y > 0
template <typename T>
T bmod(T x, T y) {
T r = x % y;
return (r < 0 ? r + y : r);
}
// require y > 0
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = x / y, r = x % y;
if (r < 0) --q, r += y;
return {q, r};
}
constexpr auto TEN = [] {
array<u64, 20> A{};
A[0] = 1;
for (int i = 1; i < 20; ++i) A[i] = 10 * A[i - 1];
return A;
}();
template <typename T, typename U>
T SUM(const U &A) {
return std::accumulate(A.begin(), A.end(), T{});
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
template <class C, class T>
inline long long LB(const C &c, const T &x) {
return lower_bound(c.begin(), c.end(), x) - c.begin();
}
template <class C, class T>
inline long long UB(const C &c, const T &x) {
return upper_bound(c.begin(), c.end(), x) - c.begin();
}
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <class T, class Container, class Compare>
T POP(priority_queue<T, Container, Compare> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
i128 binary_search(F check, i128 ok, i128 ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (1) {
i128 x = (ok + ng) / 2;
if (x == ok || x == ng) break;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
T c = max<T>(a, b);
bool changed = (c != a);
a = c;
return changed;
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
T c = min<T>(a, b);
bool changed = (c != a);
a = c;
return changed;
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vc<T> cumsum(const vc<U> &A, int off = 1) {
int N = A.size();
vc<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vc<int> argsort(const vc<T> &A) {
vc<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &...others) {
first.reserve(first.size() + (others.size() + ... + 0));
(first.insert(first.end(), others.begin(), others.end()), ...);
}
// i128
template <class T, enable_if_t<is_same_v<T, i128>, int> = 0>
constexpr i128 abs(T x) {
return x < 0 ? -x : x;
}
constexpr i128 gcd(i128 a, i128 b) {
while (b != 0) {
i128 c = a % b;
a = b, b = c;
}
return abs(a);
}
#endif
#line 1 "other/io.hpp"
#define FASTIO
// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
bool input_eof = false;
template <class T>
constexpr bool is_signed_integer_v = is_signed_v<T> || is_same_v<T, i128>;
template <class T>
struct unsigned_integer {
using type = make_unsigned_t<T>;
};
template <>
struct unsigned_integer<i128> {
using type = u128;
};
template <>
struct unsigned_integer<u128> {
using type = u128;
};
template <class T>
using unsigned_integer_t = typename unsigned_integer<T>::type;
[[noreturn]] inline void input_error(const char *message) {
fputs(message, stderr);
fputc('\n', stderr);
exit(EXIT_FAILURE);
}
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
uint32_t n = pir - pil;
memmove(ibuf, ibuf + pil, n);
pil = 0;
pir = n;
if (input_eof) return;
pir += fread(ibuf + pir, 1, SZ - pir, stdin);
if (ferror(stdin)) input_error("fastio: input error");
if (feof(stdin)) {
input_eof = true;
// Allows the last token to end exactly at EOF without a trailing
// whitespace.
if (pir < SZ) ibuf[pir++] = '\n';
}
}
inline char get_char() {
if (pil == pir) {
load();
if (pil == pir) input_error("fastio: unexpected EOF");
}
return ibuf[pil++];
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do c = get_char();
while (isspace(static_cast<unsigned char>(c)));
}
void rd(string &x) {
x.clear();
char c;
do c = get_char();
while (isspace(static_cast<unsigned char>(c)));
do {
x += c;
c = get_char();
} while (!isspace(static_cast<unsigned char>(c)));
}
template <typename T>
void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T>
void rd_integer_slow(T &x) {
char c;
do c = get_char();
while (c < '-');
bool minus = 0;
if constexpr (is_signed_integer_v<T>) {
if (c == '-') {
minus = 1, c = get_char();
}
}
x = 0;
assert('0' <= c && c <= '9');
while ('0' <= c && c <= '9') {
x = x * 10 + (c & 15), c = get_char();
}
assert(isspace(static_cast<unsigned char>(c)));
if constexpr (is_signed_integer_v<T>) {
if (minus) x = -x;
}
}
template <typename T>
void rd_integer(T &x) {
if (pil + 100 > pir) {
load();
if (pil + 100 > pir) {
rd_integer_slow(x);
return;
}
}
char c;
do c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed_integer_v<T>) {
if (c == '-') {
minus = 1, c = ibuf[pil++];
}
}
x = 0;
assert('0' <= c && c <= '9');
while ('0' <= c && c <= '9') {
x = x * 10 + (c & 15), c = ibuf[pil++];
}
assert(isspace(static_cast<unsigned char>(c)));
if constexpr (is_signed_integer_v<T>) {
if (minus) x = -x;
}
}
template <class T>
enable_if_t<is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>> rd(
T &x) {
rd_integer(x);
}
template <class T>
enable_if_t<is_floating_point_v<T> || is_same_v<T, f128>> rd(T &x) {
rd_real(x);
}
template <class T, class U>
void rd(pair<T, U> &p) {
rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
if constexpr (N < tuple_size<T>::value) {
auto &x = get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T>
void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <class T, size_t N>
void rd(array<T, N> &x) {
for (auto &d : x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
for (auto &d : x) rd(d);
}
template <class... T>
void read(T &...x) {
(rd(x), ...);
}
inline void wt_range(const char *s, size_t n) {
size_t i = 0;
while (i < n) {
if (por == SZ) flush();
size_t chunk = min(n - i, (size_t)(SZ - por));
memcpy(obuf + por, s + i, chunk);
por += chunk;
i += chunk;
}
}
void wt(const char c) {
if (por == SZ) flush();
obuf[por++] = c;
}
void wt(const char *s) { wt_range(s, strlen(s)); }
void wt(const string &s) { wt_range(s.data(), s.size()); }
template <typename T>
void wt_integer(T x) {
if (por > SZ - 100) flush();
using U = unsigned_integer_t<T>;
U y = static_cast<U>(x);
if constexpr (is_signed_integer_v<T>) {
if (x < 0) {
obuf[por++] = '-';
y = U(0) - y;
}
}
int outi;
for (outi = 96; y >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[y % 10000], 4);
y /= 10000;
}
if (y >= 1000) {
memcpy(obuf + por, pre.num[y], 4);
por += 4;
} else if (y >= 100) {
memcpy(obuf + por, pre.num[y] + 1, 3);
por += 3;
} else if (y >= 10) {
int q = (y * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (y - q * 10) | '0';
por += 2;
} else
obuf[por++] = y | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
inline void wt_real(T x) {
static char buf[1000];
int n = std::snprintf(buf, sizeof(buf), "%.15f", (double)x);
wt_range(buf, (size_t)n);
}
template <class T>
enable_if_t<is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>> wt(
T x) {
wt_integer(x);
}
template <class T>
enable_if_t<is_floating_point_v<T> || is_same_v<T, f128>> wt(T x) {
wt_real(x);
}
inline void wt(bool b) { wt(static_cast<char>('0' + (b ? 1 : 0))); }
template <class T, class U>
void wt(const pair<T, U> &val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T &t) {
if constexpr (N < tuple_size<T>::value) {
if constexpr (N > 0) wt(' ');
wt(get<N>(t));
wt_tuple<N + 1>(t);
}
}
template <class... T>
void wt(const tuple<T...> &tpl) {
wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> &val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
template <class T>
void wt(const vector<T> &val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&...tail) {
wt(forward<Head>(head));
((wt(' '), wt(forward<Tail>(tail))), ...);
wt('\n');
}
// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::flush;
using fastio::print;
using fastio::read;
#if defined(LOCAL)
#define HDR "[DEBUG:", __func__, __LINE__, "]"
#define SHOW(...) \
SHOW_IMPL(__VA_ARGS__, SHOW8, SHOW7, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, \
SHOW1) \
(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, _7, _8, NAME, ...) NAME
#define SHOW1(x) print(HDR, #x, "=", (x)), flush()
#define SHOW2(x, y) print(HDR, #x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) \
print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) \
print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v) \
print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \
(v)), \
flush()
#define SHOW6(x, y, z, w, v, u) \
print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \
(v), #u, "=", (u)), \
flush()
#define SHOW7(x, y, z, w, v, u, t) \
print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \
(v), #u, "=", (u), #t, "=", (t)), \
flush()
#define SHOW8(x, y, z, w, v, u, t, s) \
print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \
(v), #u, "=", (u), #t, "=", (t), #s, "=", (s)), \
flush()
#else
#define SHOW(...)
#endif
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__)
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
void YA(bool t = 1) { print(t ? "YA" : "TIDAK"); }
void TIDAK(bool t = 1) { YA(!t); }
void Alice(bool t = 1) { print(t ? "Alice" : "Bob"); }
void Bob(bool t = 1) { Alice(!t); }
#line 4 "test/3_yukicoder/1600_2.test.cpp"
#line 1 "other/bit.hpp"
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T kth_bit(int k) {
assert(0 <= k && k < int(8 * sizeof(T)));
return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
assert(0 <= k && k < int(8 * sizeof(T)));
return x >> k & 1;
}
template <typename UINT>
struct all_bit {
static_assert(is_unsigned<UINT>::value);
UINT s;
all_bit(UINT s) : s(s) {}
struct iter {
UINT s;
int operator*() const { return lowbit(s); }
void operator++() { s &= s - 1; }
bool operator!=(nullptr_t) const { return s; }
};
iter begin() const { return {s}; }
nullptr_t end() const { return nullptr; }
};
template <typename UINT>
struct all_subset {
static_assert(is_unsigned<UINT>::value);
UINT s;
all_subset(UINT s) : s(s) {}
struct iter {
UINT s, t;
bool done = false;
UINT operator*() const { return t; }
void operator++() {
done = (t == 0);
t = (t - 1) & s;
}
bool operator!=(nullptr_t) const { return !done; }
};
iter begin() const { return {s, s}; }
nullptr_t end() const { return nullptr; }
};
constexpr u64 full_mask(int n) {
assert(0 <= n && n <= 64);
return n == 64 ? -1ULL : (1ULL << n) - 1;
}
u64 bit_reverse(u64 x) {
x = ((x & 0x5555555555555555ULL) << 1) | ((x >> 1) & 0x5555555555555555ULL);
x = ((x & 0x3333333333333333ULL) << 2) | ((x >> 2) & 0x3333333333333333ULL);
x = ((x & 0x0f0f0f0f0f0f0f0fULL) << 4) | ((x >> 4) & 0x0f0f0f0f0f0f0f0fULL);
x = ((x & 0x00ff00ff00ff00ffULL) << 8) | ((x >> 8) & 0x00ff00ff00ff00ffULL);
x = ((x & 0x0000ffff0000ffffULL) << 16) | ((x >> 16) & 0x0000ffff0000ffffULL);
x = (x << 32) | (x >> 32);
return x;
}
#line 2 "ds/bit_vector.hpp"
struct Bit_Vector {
int n;
bool prepared = 0;
vc<pair<u64, u32>> dat;
Bit_Vector(int n = 0) : n(n) { dat.assign((n + 127) >> 6, {0, 0}); }
void set(int i) {
assert(!prepared && (0 <= i && i < n));
dat[i >> 6].fi |= u64(1) << (i & 63);
}
void reset() {
fill(all(dat), pair<u64, u32>{0, 0});
prepared = 0;
}
void build() {
prepared = 1;
FOR(i, len(dat) - 1) dat[i + 1].se = dat[i].se + popcnt(dat[i].fi);
}
bool operator[](int i) const { return dat[i >> 6].fi >> (i & 63) & 1; }
// [0, k) 内の 1 の個数
int count_prefix(int k, bool f = true) const {
assert(prepared);
auto [a, b] = dat[k >> 6];
int ret = b + popcnt(a & ((u64(1) << (k & 63)) - 1));
return (f ? ret : k - ret);
}
int count(int L, int R, bool f = true) const {
return count_prefix(R, f) - count_prefix(L, f);
}
string to_string() const {
string ans;
FOR(i, n) ans += '0' + (dat[i / 64].fi >> (i % 64) & 1);
return ans;
}
};
#line 1 "alg/monoid/dummy.hpp"
struct Monoid_Dummy {
using value_type = char;
static constexpr bool commute = true;
static value_type op(value_type, value_type) { return 0; }
static value_type id() { return 0; }
};
#line 2 "ds/dummy_data_structure.hpp"
struct Dummy_Data_Structure {
using MX = Monoid_Dummy;
using T = typename MX::value_type;
void build(const vc<T>& A) {}
};
#line 3 "ds/wavelet_matrix/wavelet_matrix.hpp"
template <typename Y, typename SEGTREE>
struct Uncompressed_Wavelet_Matrix {
using Mono = typename SEGTREE::MX;
using T = typename Mono::value_type;
static_assert(Mono::commute);
static_assert(is_same_v<Y, int> || is_same_v<Y, ll>);
int n = 0, log = 0;
vc<int> mid;
vc<Bit_Vector> bv;
vc<SEGTREE> seg;
Y limit;
Uncompressed_Wavelet_Matrix() = default;
// f(i) = {A[i], dat[i]}
template <typename F>
Uncompressed_Wavelet_Matrix(int n, F f, int log = -1) {
build(n, f, log);
}
Uncompressed_Wavelet_Matrix(const vc<Y>& A, int log = -1) {
static_assert(is_same_v<SEGTREE, Dummy_Data_Structure>);
build(len(A), [&](int i) -> pair<Y, T> { return {A[i], Mono::id()}; }, log);
}
template <typename F>
void build(int n, F f, int log = -1) {
this->n = n;
vc<Y> A(n);
vc<T> S(n);
FOR(i, n) tie(A[i], S[i]) = f(i);
if (log == -1) {
log = (n == 0 ? 0 : topbit(MAX(A)) + 1);
} else {
for (auto& x : A) assert(0 <= x && topbit(x) < log);
}
this->log = log;
limit = Y(1) << log;
if constexpr (is_same_v<Y, int>) assert(0 <= log && log <= 30);
if constexpr (is_same_v<Y, ll>) assert(0 <= log && log <= 62);
mid.resize(log), bv.assign(log, Bit_Vector(n));
vc<Y> A0(n), A1(n);
vc<T> S0(n), S1(n);
seg.resize(log + 1);
seg[log].build(S);
for (int d = log - 1; d >= 0; --d) {
int p0 = 0, p1 = 0;
for (int i = 0; i < n; ++i) {
if (A[i] >> d & 1) {
bv[d].set(i), A1[p1] = A[i], S1[p1] = S[i], p1++;
} else {
A0[p0] = A[i], S0[p0] = S[i], p0++;
}
}
swap(A, A0), swap(S, S0);
move(A1.begin(), A1.begin() + p1, A.begin() + p0);
move(S1.begin(), S1.begin() + p1, S.begin() + p0);
mid[d] = p0, bv[d].build(), seg[d].build(S);
}
}
tuple<int, int, int, int> get_subtree(int d, int L, int R) const {
assert(1 <= d && d <= log);
int a = bv[d - 1].count_prefix(L), b = bv[d - 1].count_prefix(R);
return {L - a, R - b, mid[d - 1] + a, mid[d - 1] + b};
}
template <typename F>
void work_point(F f, int i) {
assert(0 <= i && i < n);
f(log, i);
FOR_R(d, log) {
int a = bv[d].count_prefix(i);
if (bv[d][i]) {
i = mid[d] + a;
} else {
i = i - a;
}
f(d, i);
}
}
template <typename F>
void work_prefix(F f, int L, int R, Y y) const {
chmin(y, limit);
if (y == 0) return;
if (y == limit) {
f(log, L, R);
return;
}
FOR_R(d, log) {
auto [L0, R0, L1, R1] = get_subtree(d + 1, L, R);
if (y >> d & 1) {
f(d, L0, R0);
L = L1, R = R1;
} else {
L = L0, R = R0;
}
}
}
template <typename F>
void work_range(F f, int L, int R, Y y1, Y y2) const {
chmin(y2, limit);
if (y1 >= y2) return;
assert(0 <= y1 && y1 <= y2 && y2 <= limit);
if (y1 == 0) return work_prefix(f, L, R, y2);
auto dfs = [&](auto& dfs, int d, int L, int R, Y y1, Y y2) -> void {
if (y1 == y2) return;
if (y1 == 0 && y2 == Y(1) << d) {
f(d, L, R);
return;
}
assert(d > 0);
auto [L0, R0, L1, R1] = get_subtree(d, L, R);
Y m = (Y(1) << (d - 1));
if (y2 <= m) {
dfs(dfs, d - 1, L0, R0, y1, y2);
} else if (y1 >= m) {
dfs(dfs, d - 1, L1, R1, y1 - m, y2 - m);
} else {
dfs(dfs, d - 1, L0, R0, y1, m);
dfs(dfs, d - 1, L1, R1, 0, y2 - m);
}
};
dfs(dfs, log, L, R, y1, y2);
}
// [L,R) x [0,y)
int prefix_count(int L, int R, Y y) const {
int cnt = 0;
work_prefix([&](int d, int a, int b) { cnt += b - a; }, L, R, y);
return cnt;
}
// [L,R) x [y1,y2)
int count(int L, int R, Y y1, Y y2) const {
return prefix_count(L, R, y2) - prefix_count(L, R, y1);
}
// [L,R) x [0,y)
T prefix_prod(int L, int R, Y y) const {
T ans = Mono::id();
work_prefix(
[&](int d, int a, int b) { ans = Mono::op(ans, seg[d].prod(a, b)); }, L,
R, y);
return ans;
}
// [L,R) x [y1,y2)
T prod(int L, int R, Y y1, Y y2) const {
T ans = Mono::id();
work_range(
[&](int d, int a, int b) { ans = Mono::op(ans, seg[d].prod(a, b)); }, L,
R, y1, y2);
return ans;
}
T prod_all(int L, int R) const { return seg[log].prod(L, R); }
// [L,R) x [0,y)
pair<int, T> prefix_count_and_prod(int L, int R, Y y) const {
pair<int, T> ans = {0, Mono::id()};
work_prefix(
[&](int d, int a, int b) {
ans.fi += b - a;
ans.se = Mono::op(ans.se, seg[d].prod(a, b));
},
L, R, y);
return ans;
}
// [L,R) x [y1,y2)
pair<int, T> count_and_prod(int L, int R, Y y1, Y y2) const {
pair<int, T> ans = {0, Mono::id()};
work_range(
[&](int d, int a, int b) {
ans.fi += b - a;
ans.se = Mono::op(ans.se, seg[d].prod(a, b));
},
L, R, y1, y2);
return ans;
}
Y kth(int L, int R, int k) const {
assert(0 <= k && k < R - L);
Y ans = 0;
for (int d = log - 1; d >= 0; --d) {
auto [L0, R0, L1, R1] = get_subtree(d + 1, L, R);
if (k < R0 - L0) {
L = L0, R = R0;
} else {
ans |= Y(1) << d;
k -= R0 - L0, L = L1, R = R1;
}
}
return ans;
}
template <bool upper>
Y median(int L, int R) const {
assert(0 <= L && L < R && R <= n);
int k = (upper ? (R - L) / 2 : (R - L - 1) / 2);
return kth(L, R, k);
}
void set(int i, T t) {
assert(0 <= i && i < n);
work_point([&](int d, int i) { seg[d].set(i, t); }, i);
}
void multiply(int i, T t) {
assert(0 <= i && i < n);
work_point([&](int d, int i) { seg[d].multiply(i, t); }, i);
}
void add(int i, T t) {
assert(0 <= i && i < n);
work_point([&](int d, int i) { seg[d].add(i, t); }, i);
}
// [L,R) x [0,y) での check(y, cnt, prod) が true となる最大の (Y,cnt,prod)
// cnt はデータ件数全体であって, activate/deactivate を考慮する場合には
// prod の方を見る必要がある
template <typename F>
tuple<Y, int, T> max_right(F check, int L, int R) const {
int cnt = 0;
Y y = 0;
T t = Mono::id();
T t_all = seg[log].prod(L, R);
assert(check(0, 0, Mono::id()));
if (check(infty<Y>, R - L, t_all)) {
return {infty<Y>, R - L, t_all};
}
for (int d = log - 1; d >= 0; --d) {
auto [L0, R0, L1, R1] = get_subtree(d + 1, L, R);
Y y1 = y | Y(1) << d;
int cnt1 = cnt + R0 - L0;
T t1 = Mono::op(t, seg[d].prod(L0, R0));
if (check(y1, cnt1, t1)) {
y = y1, cnt = cnt1, t = t1, L = L1, R = R1;
} else {
L = L0, R = R0;
}
}
return {y, cnt, t};
}
// [L,R) x [0,y) での check(y, cnt, prod) が true となる最大の (Y,cnt,prod)
template <typename F>
tuple<Y, int, T> max_right_many(F check, vc<pair<int, int>> LR) const {
int cnt = 0;
Y y = 0;
T t = Mono::id();
T t_all = Mono::id();
int cnt_all = 0;
for (auto& [l, r] : LR)
t_all = Mono::op(t_all, prod_all(l, r)), cnt_all += r - l;
assert(check(0, 0, Mono::id()));
if (check(infty<Y>, cnt_all, t_all)) {
return {infty<Y>, cnt_all, t_all};
}
for (int d = log - 1; d >= 0; --d) {
Y y1 = Y(1) << d;
T t1 = t;
int cnt1 = 0;
for (auto& [L, R] : LR) {
auto [L0, R0, L1, R1] = get_subtree(d + 1, L, R);
cnt1 += R0 - L0;
t1 = Mono::op(t1, seg[d].prod(L0, R0));
}
if (check(y1, cnt1, t1)) {
y = y1, cnt = cnt1, t = t1;
for (auto& [L, R] : LR) {
auto [L0, R0, L1, R1] = get_subtree(d + 1, L, R);
L = L1, R = R1;
}
} else {
for (auto& [L, R] : LR) {
auto [L0, R0, L1, R1] = get_subtree(d + 1, L, R);
L = L0, R = R0;
}
}
}
return {y, cnt, t};
}
// [L,R) x [y, inf) での check(y, cnt, prod) が true となる最小の (y,cnt,prod)
// cnt==0 だと true であることは仮定する
// https://qoj.ac/contest/1047/problem/5094
template <typename F>
tuple<Y, int, T> min_left_many(F check, vc<pair<int, int>> LR) const {
assert(check(limit, 0, Mono::id()));
int cnt = 0;
Y y = limit;
T t = Mono::id();
T t_all = Mono::id();
int cnt_all = 0;
for (auto& [l, r] : LR)
t_all = Mono::op(t_all, prod_all(l, r)), cnt_all += r - l;
if (check(0, cnt_all, t_all)) {
return {0, cnt_all, t_all};
}
for (int d = log - 1; d >= 0; --d) {
Y y1 = y - (Y(1) << d);
T t1 = t;
int cnt1 = cnt;
for (auto& [L, R] : LR) {
auto [L0, R0, L1, R1] = get_subtree(d + 1, L, R);
cnt1 += R1 - L1;
t1 = Mono::op(t1, seg[d].prod(L1, R1));
}
if (check(y1, cnt1, t1)) {
y = y1, cnt = cnt1, t = t1;
SHOW(y);
for (auto& [L, R] : LR) {
auto [L0, R0, L1, R1] = get_subtree(d + 1, L, R);
L = L0, R = R0;
}
} else {
for (auto& [L, R] : LR) {
auto [L0, R0, L1, R1] = get_subtree(d + 1, L, R);
L = L1, R = R1;
}
}
}
SHOW(y, cnt, t);
return {y, cnt, t};
}
};
template <typename Y, typename SEGTREE>
struct Compressed_Wavelet_Matrix {
using Mono = typename SEGTREE::MX;
using T = typename Mono::value_type;
int n = 0;
vc<Y> key;
Uncompressed_Wavelet_Matrix<int, SEGTREE> wm;
Compressed_Wavelet_Matrix() = default;
// f(i) = {A[i], dat[i]}
template <typename F>
Compressed_Wavelet_Matrix(int n, F f) {
build(n, f);
}
Compressed_Wavelet_Matrix(const vc<Y>& A) {
static_assert(is_same_v<SEGTREE, Dummy_Data_Structure>);
build(A);
}
template <typename F>
void build(int n, F f) {
this->n = n;
vc<Y> A(n);
vc<T> S(n);
FOR(i, n) tie(A[i], S[i]) = f(i);
key = A;
UNIQUE(key);
wm.build(n, [&](int i) -> pair<int, T> {
int k = LB(key, A[i]);
return {k, S[i]};
});
}
void build(const vc<Y>& A) {
static_assert(is_same_v<SEGTREE, Dummy_Data_Structure>);
n = len(A);
key = A;
UNIQUE(key);
wm.build(n, [&](int i) -> pair<int, T> {
int k = LB(key, A[i]);
return {k, Mono::id()};
});
}
Y kth(int L, int R, int k) const { return key[wm.kth(L, R, k)]; }
template <bool upper>
Y median(int L, int R) const {
return key[wm.template median<upper>(L, R)];
}
// [L,R) x [-inf,y)
int prefix_count(int L, int R, Y y) const {
return wm.prefix_count(L, R, LB(key, y));
}
// [L,R) x [y1,y2)
int count(int L, int R, Y y1, Y y2) const {
return wm.count(L, R, LB(key, y1), LB(key, y2));
}
// [L,R) x [-inf,y)
T prefix_prod(int L, int R, Y y) const {
return wm.prefix_prod(L, R, LB(key, y));
}
// [L,R) x [y1,y2)
T prod(int L, int R, Y y1, Y y2) const {
return wm.prod(L, R, LB(key, y1), LB(key, y2));
}
T prod_all(int L, int R) const { return wm.prod_all(L, R); }
// [L,R) x [-inf,y)
pair<int, T> prefix_count_and_prod(int L, int R, Y y) const {
return wm.prefix_count_and_prod(L, R, LB(key, y));
}
// [L,R) x [y1,y2)
pair<int, T> count_and_prod(int L, int R, Y y1, Y y2) const {
return wm.count_and_prod(L, R, LB(key, y1), LB(key, y2));
}
void set(int i, T t) { wm.set(i, t); }
void multiply(int i, T t) { wm.multiply(i, t); }
void add(int i, T t) { wm.add(i, t); }
};
template <typename Y, bool compress, typename SEGTREE = Dummy_Data_Structure>
using Wavelet_Matrix =
conditional_t<compress, Compressed_Wavelet_Matrix<Y, SEGTREE>,
Uncompressed_Wavelet_Matrix<Y, SEGTREE>>;
#line 1 "ds/index_compression.hpp"
template <typename T>
struct Index_Compression_DISTINCT_SMALL {
int mi, ma;
vc<T> dat;
vc<T> build(vc<int> X) {
mi = 0, ma = -1;
if (!X.empty()) mi = MIN(X), ma = MAX(X);
dat.assign(ma - mi + 2, 0);
for (auto& x : X) dat[x - mi + 1]++;
FOR(i, len(dat) - 1) dat[i + 1] += dat[i];
for (auto& x : X) {
x = dat[x - mi]++;
}
FOR_R(i, 1, len(dat)) dat[i] = dat[i - 1];
dat[0] = 0;
return X;
}
int size() const { return len(dat); }
int val_to_idx(T x) const { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; }
int idx_to_val(int i) const { return dat[i]; }
};
template <typename T>
struct Index_Compression_SAME_SMALL {
int mi, ma;
vc<T> dat;
vc<T> build(vc<T> X) {
mi = 0, ma = -1;
if (!X.empty()) mi = MIN(X), ma = MAX(X);
dat.assign(ma - mi + 2, 0);
for (auto& x : X) dat[x - mi + 1] = 1;
FOR(i, len(dat) - 1) dat[i + 1] += dat[i];
for (auto& x : X) {
x = dat[x - mi];
}
return X;
}
int size() const { return len(dat); }
int val_to_idx(T x) const { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; }
int idx_to_val(int i) const { return dat[i]; }
};
template <typename T>
struct Index_Compression_SAME_LARGE {
vc<T> dat;
vc<int> build(const vc<T>& X) {
dat.reserve(len(X));
vc<pair<T, int>> tmp(len(X));
FOR(i, len(X)) tmp[i] = {X[i], i};
sort(all(tmp));
vc<int> ANS(len(X));
for (auto [x, j] : tmp) {
if (dat.empty() || dat.back() != x) dat.eb(x);
ANS[j] = len(dat) - 1;
}
return ANS;
}
int size() const { return len(dat); }
int val_to_idx(T x) const { return LB(dat, x); }
int idx_to_val(int i) const { return dat[i]; }
};
template <typename T>
struct Index_Compression_DISTINCT_LARGE {
vc<T> dat;
vc<int> build(vc<T> X) {
dat.reserve(len(X));
vc<pair<T, int>> tmp(len(X));
FOR(i, len(X)) tmp[i] = {X[i], i};
sort(all(tmp));
vc<int> ANS(len(X));
for (auto [x, j] : tmp) {
dat.eb(x);
ANS[j] = len(dat) - 1;
}
return ANS;
}
int size() const { return len(dat); }
int val_to_idx(T x) const { return LB(dat, x); }
int idx_to_val(int i) const { return dat[i]; }
};
template <typename T, bool SMALL>
using Index_Compression_DISTINCT =
typename std::conditional<SMALL, Index_Compression_DISTINCT_SMALL<T>,
Index_Compression_DISTINCT_LARGE<T>>::type;
template <typename T, bool SMALL>
using Index_Compression_SAME =
typename std::conditional<SMALL, Index_Compression_SAME_SMALL<T>,
Index_Compression_SAME_LARGE<T>>::type;
// SAME: [2,3,2] -> [0,1,0]
// DISTINCT: [2,2,3] -> [0,2,1]
// build で列を圧縮してくれる. そのあと
// (x): lower_bound(X,x) をかえす
template <typename T, bool SAME, bool SMALL>
using Index_Compression =
typename std::conditional<SAME, Index_Compression_SAME<T, SMALL>,
Index_Compression_DISTINCT<T, SMALL>>::type;
#line 3 "ds/wavelet_matrix/wavelet_matrix_2d_range.hpp"
template <typename XY, bool compress_X, bool compress_Y,
typename SEGTREE = Dummy_Data_Structure>
struct Wavelet_Matrix_2D_Range {
// 点群を X 昇順に並べる.
Wavelet_Matrix<XY, compress_Y, SEGTREE> WM;
using Mono = typename SEGTREE::MX;
using T = typename Mono::value_type;
static_assert(Mono::commute);
Index_Compression<XY, false, !compress_X> IDX_X;
int n;
vc<int> new_idx;
template <typename F>
Wavelet_Matrix_2D_Range(int n, F f) {
build(n, f);
}
template <typename F>
void build(int m, F f) {
n = m;
vc<XY> X(n), Y(n);
vc<T> S(n);
FOR(i, n) {
auto tmp = f(i);
X[i] = get<0>(tmp), Y[i] = get<1>(tmp), S[i] = get<2>(tmp);
}
new_idx = IDX_X.build(X);
vc<int> I(n);
FOR(i, n) I[new_idx[i]] = i;
Y = rearrange(Y, I);
S = rearrange(S, I);
WM.build(n, [&](int i) -> pair<XY, T> { return {Y[i], S[i]}; });
}
int count(XY x1, XY x2, XY y1, XY y2) {
return WM.count(IDX_X.val_to_idx(x1), IDX_X.val_to_idx(x2), y1, y2);
}
// [L,R) x [-inf,y)
pair<int, T> prefix_count_and_prod(XY x1, XY x2, XY y) {
return WM.prefix_count_and_prod(IDX_X.val_to_idx(x1), IDX_X.val_to_idx(x2),
y);
}
// [L,R) x [y1,y2)
pair<int, T> count_and_prod(XY x1, XY x2, XY y1, XY y2) {
return WM.count_and_prod(IDX_X.val_to_idx(x1), IDX_X.val_to_idx(x2), y1,
y2);
}
// [L,R) x [-inf,inf)
T prod_all(XY x1, XY x2) {
return WM.prod_all(IDX_X.val_to_idx(x1), IDX_X.val_to_idx(x2));
}
// [L,R) x [-inf,y)
T prefix_prod(XY x1, XY x2, XY y) {
return WM.prefix_prod(IDX_X.val_to_idx(x1), IDX_X.val_to_idx(x2), y);
}
// [L,R) x [y1,y2)
T prod(XY x1, XY x2, XY y1, XY y2) {
return WM.prod(IDX_X.val_to_idx(x1), IDX_X.val_to_idx(x2), y1, y2);
}
// i は最初に渡したインデックス
void set(int i, T t) { WM.set(new_idx[i], t); }
// i は最初に渡したインデックス
void multiply(int i, T t) { WM.multiply(new_idx[i], t); }
void add(int i, T t) { WM.multiply(new_idx[i], t); }
// [L,R) x [0,y) での check(y, cnt, prod) が true となる最大の (Y,cnt,prod)
// cnt はデータ件数全体であって, activate/deactivate を考慮する場合には
// prod の方を見る必要がある
template <typename F>
tuple<XY, int, T> max_right(F check, XY x1, XY x2) const {
return WM.max_right(check, IDX_X.val_to_idx(x1), IDX_X.val_to_idx(x2));
}
};
#line 1 "other/bit.hpp"
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T kth_bit(int k) {
assert(0 <= k && k < int(8 * sizeof(T)));
return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
assert(0 <= k && k < int(8 * sizeof(T)));
return x >> k & 1;
}
template <typename UINT>
struct all_bit {
static_assert(is_unsigned<UINT>::value);
UINT s;
all_bit(UINT s) : s(s) {}
struct iter {
UINT s;
int operator*() const { return lowbit(s); }
void operator++() { s &= s - 1; }
bool operator!=(nullptr_t) const { return s; }
};
iter begin() const { return {s}; }
nullptr_t end() const { return nullptr; }
};
template <typename UINT>
struct all_subset {
static_assert(is_unsigned<UINT>::value);
UINT s;
all_subset(UINT s) : s(s) {}
struct iter {
UINT s, t;
bool done = false;
UINT operator*() const { return t; }
void operator++() {
done = (t == 0);
t = (t - 1) & s;
}
bool operator!=(nullptr_t) const { return !done; }
};
iter begin() const { return {s, s}; }
nullptr_t end() const { return nullptr; }
};
constexpr u64 full_mask(int n) {
assert(0 <= n && n <= 64);
return n == 64 ? -1ULL : (1ULL << n) - 1;
}
u64 bit_reverse(u64 x) {
x = ((x & 0x5555555555555555ULL) << 1) | ((x >> 1) & 0x5555555555555555ULL);
x = ((x & 0x3333333333333333ULL) << 2) | ((x >> 2) & 0x3333333333333333ULL);
x = ((x & 0x0f0f0f0f0f0f0f0fULL) << 4) | ((x >> 4) & 0x0f0f0f0f0f0f0f0fULL);
x = ((x & 0x00ff00ff00ff00ffULL) << 8) | ((x >> 8) & 0x00ff00ff00ff00ffULL);
x = ((x & 0x0000ffff0000ffffULL) << 16) | ((x >> 16) & 0x0000ffff0000ffffULL);
x = (x << 32) | (x >> 32);
return x;
}
#line 2 "ds/sparse_table/sparse_table.hpp"
// 冪等なモノイドであることを仮定。disjoint sparse table より x 倍高速
template <class Monoid>
struct Sparse_Table {
using MX = Monoid;
using X = typename MX::value_type;
int n, log;
vvc<X> dat;
Sparse_Table() {}
Sparse_Table(int n) { build(n); }
template <typename F>
Sparse_Table(int n, F f) {
build(n, f);
}
Sparse_Table(const vc<X>& v) { build(v); }
void build(int m) {
build(m, [](int i) -> X { return MX::id(); });
}
void build(const vc<X>& v) {
build(len(v), [&](int i) -> X { return v[i]; });
}
template <typename F>
void build(int m, F f) {
n = m, log = 1;
while ((1 << log) < n) ++log;
dat.resize(log);
dat[0].resize(n);
FOR(i, n) dat[0][i] = f(i);
FOR(i, log - 1) {
dat[i + 1].resize(len(dat[i]) - (1 << i));
FOR(j, len(dat[i]) - (1 << i)) {
dat[i + 1][j] = MX::op(dat[i][j], dat[i][j + (1 << i)]);
}
}
}
X prod(int L, int R) const {
if (L == R) return MX::id();
if (R == L + 1) return dat[0][L];
int k = topbit(R - L - 1);
return MX::op(dat[k][L], dat[k][R - (1 << k)]);
}
template <class F>
int max_right(const F check, int L) const {
assert(0 <= L && L <= n && check(MX::id()));
if (L == n) return n;
int ok = L, ng = n + 1;
while (ok + 1 < ng) {
int k = (ok + ng) / 2;
bool bl = check(prod(L, k));
if (bl) ok = k;
if (!bl) ng = k;
}
return ok;
}
template <class F>
int min_left(const F check, int R) const {
assert(0 <= R && R <= n && check(MX::id()));
if (R == 0) return 0;
int ok = R, ng = -1;
while (ng + 1 < ok) {
int k = (ok + ng) / 2;
bool bl = check(prod(k, R));
if (bl) ok = k;
if (!bl) ng = k;
}
return ok;
}
};
#line 1 "other/bit.hpp"
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T kth_bit(int k) {
assert(0 <= k && k < int(8 * sizeof(T)));
return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
assert(0 <= k && k < int(8 * sizeof(T)));
return x >> k & 1;
}
template <typename UINT>
struct all_bit {
static_assert(is_unsigned<UINT>::value);
UINT s;
all_bit(UINT s) : s(s) {}
struct iter {
UINT s;
int operator*() const { return lowbit(s); }
void operator++() { s &= s - 1; }
bool operator!=(nullptr_t) const { return s; }
};
iter begin() const { return {s}; }
nullptr_t end() const { return nullptr; }
};
template <typename UINT>
struct all_subset {
static_assert(is_unsigned<UINT>::value);
UINT s;
all_subset(UINT s) : s(s) {}
struct iter {
UINT s, t;
bool done = false;
UINT operator*() const { return t; }
void operator++() {
done = (t == 0);
t = (t - 1) & s;
}
bool operator!=(nullptr_t) const { return !done; }
};
iter begin() const { return {s, s}; }
nullptr_t end() const { return nullptr; }
};
constexpr u64 full_mask(int n) {
assert(0 <= n && n <= 64);
return n == 64 ? -1ULL : (1ULL << n) - 1;
}
u64 bit_reverse(u64 x) {
x = ((x & 0x5555555555555555ULL) << 1) | ((x >> 1) & 0x5555555555555555ULL);
x = ((x & 0x3333333333333333ULL) << 2) | ((x >> 2) & 0x3333333333333333ULL);
x = ((x & 0x0f0f0f0f0f0f0f0fULL) << 4) | ((x >> 4) & 0x0f0f0f0f0f0f0f0fULL);
x = ((x & 0x00ff00ff00ff00ffULL) << 8) | ((x >> 8) & 0x00ff00ff00ff00ffULL);
x = ((x & 0x0000ffff0000ffffULL) << 16) | ((x >> 16) & 0x0000ffff0000ffffULL);
x = (x << 32) | (x >> 32);
return x;
}
#line 2 "ds/sparse_table/disjoint_sparse_table.hpp"
template <class Monoid>
struct Disjoint_Sparse_Table {
using MX = Monoid;
using X = typename MX::value_type;
int n, log;
vvc<X> dat;
Disjoint_Sparse_Table() {}
Disjoint_Sparse_Table(int n) { build(n); }
template <typename F>
Disjoint_Sparse_Table(int n, F f) {
build(n, f);
}
Disjoint_Sparse_Table(const vc<X>& v) { build(v); }
void build(int m) {
build(m, [](int i) -> X { return MX::id(); });
}
void build(const vc<X>& v) {
build(len(v), [&](int i) -> X { return v[i]; });
}
template <typename F>
void build(int m, F f) {
n = m, log = 1;
while ((1 << log) < n) ++log;
dat.resize(log);
dat[0].reserve(n);
FOR(i, n) dat[0].eb(f(i));
FOR(i, 1, log) {
auto& v = dat[i];
v = dat[0];
int b = 1 << i;
for (int m = b; m <= n; m += 2 * b) {
int L = m - b, R = min(n, m + b);
FOR_R(j, L + 1, m) v[j - 1] = MX::op(v[j - 1], v[j]);
FOR(j, m, R - 1) v[j + 1] = MX::op(v[j], v[j + 1]);
}
}
}
X prod(int L, int R) const {
if (L == R) return MX::id();
--R;
if (L == R) return dat[0][L];
int k = topbit(L ^ R);
return MX::op(dat[k][L], dat[k][R]);
}
template <class F>
int max_right(const F check, int L) const {
assert(0 <= L && L <= n && check(MX::id()));
if (L == n) return n;
int ok = L, ng = n + 1;
while (ok + 1 < ng) {
int k = (ok + ng) / 2;
bool bl = check(prod(L, k));
if (bl) ok = k;
if (!bl) ng = k;
}
return ok;
}
template <class F>
int min_left(const F check, int R) const {
assert(0 <= R && R <= n && check(MX::id()));
if (R == 0) return 0;
int ok = R, ng = -1;
while (ng + 1 < ok) {
int k = (ok + ng) / 2;
bool bl = check(prod(k, R));
if (bl) ok = k;
if (!bl) ng = k;
}
return ok;
}
};
#line 3 "ds/static_range_product.hpp"
/*
参考：https://judge.yosupo.jp/submission/106668
長さ 2^LOG のブロックに分ける．ブロック内の prefix, suffix を持つ．
ブロック積の列を ST(DST) で持つ．ブロックをまたぐ積は O(1).
短いものは O(1) を諦めて愚直ということにする．
前計算：O(Nlog(N)/2^LOG)
クエリ：O(1) / worst O(2^LOG)
*/
template <typename Monoid, typename SPARSE_TABLE, int LOG = 4>
struct Static_Range_Product {
using MX = Monoid;
using X = typename MX::value_type;
int N, b_num;
vc<X> A, pre, suf; // inclusive
SPARSE_TABLE ST;
Static_Range_Product() {}
template <typename F>
Static_Range_Product(int n, F f) {
build(n, f);
}
Static_Range_Product(const vc<X>& v) { build(v); }
void build(const vc<X>& v) {
build(len(v), [&](int i) -> X { return v[i]; });
}
template <typename F>
void build(int m, F f) {
N = m;
b_num = N >> LOG;
A.resize(N);
FOR(i, N) A[i] = f(i);
pre = A, suf = A;
constexpr int mask = (1 << LOG) - 1;
FOR(i, 1, N) {
if (i & mask) pre[i] = MX::op(pre[i - 1], A[i]);
}
FOR_R(i, 1, N) {
if (i & mask) suf[i - 1] = MX::op(A[i - 1], suf[i]);
}
ST.build(b_num, [&](int i) -> X { return suf[i << LOG]; });
}
// O(1) or O(R-L)
X prod(int L, int R) const {
if (L == R) return MX::id();
R -= 1;
int a = L >> LOG, b = R >> LOG;
if (a < b) {
X x = ST.prod(a + 1, b);
x = MX::op(suf[L], x);
x = MX::op(x, pre[R]);
return x;
}
X x = A[L];
FOR(i, L + 1, R + 1) x = MX::op(x, A[i]);
return x;
}
template <class F>
int max_right(const F check, int L) const {
assert(0 <= L && L <= N && check(MX::id()));
if (L == N) return N;
int ok = L, ng = N + 1;
while (ok + 1 < ng) {
int k = (ok + ng) / 2;
bool bl = check(prod(L, k));
if (bl) ok = k;
if (!bl) ng = k;
}
return ok;
}
template <class F>
int min_left(const F check, int R) const {
assert(0 <= R && R <= N && check(MX::id()));
if (R == 0) return 0;
int ok = R, ng = -1;
while (ng + 1 < ok) {
int k = (ok + ng) / 2;
bool bl = check(prod(k, R));
if (bl) ok = k;
if (!bl) ng = k;
}
return ok;
}
};
#line 7 "test/3_yukicoder/1600_2.test.cpp"
#line 1 "alg/monoid/min.hpp"
// require: all values x satisfy x <= infty<E>
template <typename E>
struct Monoid_Min {
using X = E;
using value_type = X;
static constexpr X op(const X &x, const X &y) noexcept { return min(x, y); }
static constexpr X id() { return infty<E>; }
static constexpr bool commute = true;
};
#line 1 "graph/tree.hpp"
#line 1 "ds/hashmap.hpp"
// u64 -> Val
template <typename Val>
struct HashMap {
// n は入れたいものの個数で ok
HashMap(u32 n = 0) { build(n); }
void build(u32 n) {
u32 k = 8;
while (k < n * 2) k *= 2;
cap = k / 2, mask = k - 1;
key.resize(k), val.resize(k), used.assign(k, 0);
}
// size を保ったまま. size=0 にするときは build すること.
void clear() {
used.assign(len(used), 0);
cap = (mask + 1) / 2;
}
int size() { return len(used) / 2 - cap; }
int index(const u64& k) {
int i = 0;
for (i = hash(k); used[i] && key[i] != k; i = (i + 1) & mask) {
}
return i;
}
Val& operator[](const u64& k) {
int i = index(k);
if (used[i]) return val[i];
if (cap == 0) extend(), i = index(k);
used[i] = 1, key[i] = k, val[i] = Val{}, --cap;
return val[i];
}
Val get(const u64& k, Val default_value) {
int i = index(k);
return (used[i] ? val[i] : default_value);
}
bool count(const u64& k) {
int i = index(k);
return used[i] && key[i] == k;
}
// f(key, val)
template <typename F>
void enumerate_all(F f) {
FOR(i, len(used)) if (used[i]) f(key[i], val[i]);
}
private:
u32 cap, mask;
vc<u64> key;
vc<Val> val;
vc<bool> used;
u64 hash(u64 x) {
static const u64 FIXED_RANDOM =
std::chrono::steady_clock::now().time_since_epoch().count();
x += FIXED_RANDOM;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return (x ^ (x >> 31)) & mask;
}
void extend() {
vc<pair<u64, Val>> dat;
dat.reserve(len(used) / 2 - cap);
FOR(i, len(used)) {
if (used[i]) dat.eb(key[i], val[i]);
}
build(2 * len(dat));
for (auto& [a, b] : dat) (*this)[a] = b;
}
};
#line 2 "graph/base.hpp"
template <typename T>
struct Edge {
int frm, to;
T cost;
int id;
};
template <typename T = int, bool directed = false>
struct Graph {
static constexpr bool is_directed = directed;
int N, M;
using cost_type = T;
using edge_type = Edge<T>;
vector<edge_type> edges;
vector<int> indptr;
vector<edge_type> csr_edges;
mutable vc<int> vc_deg, vc_indeg, vc_outdeg;
mutable HashMap<int> MP_FOR_EID;
bool prepared;
class OutgoingEdges {
public:
OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}
const edge_type* begin() const {
if (l == r) {
return 0;
}
return &G->csr_edges[l];
}
const edge_type* end() const {
if (l == r) {
return 0;
}
return &G->csr_edges[r];
}
private:
const Graph* G;
int l, r;
};
bool is_prepared() const { return prepared; }
Graph() : N(0), M(0), prepared(0) {}
Graph(int N) : N(N), M(0), prepared(0) {}
void build(int n) {
N = n, M = 0;
prepared = 0;
edges.clear();
indptr.clear();
csr_edges.clear();
vc_deg.clear();
vc_indeg.clear();
vc_outdeg.clear();
MP_FOR_EID.clear();
}
void add(int frm, int to, T cost = 1, int i = -1) {
assert(!prepared);
assert(0 <= frm && frm < N && 0 <= to && to < N);
if (i == -1) i = M;
auto e = edge_type({frm, to, cost, i});
edges.eb(e);
++M;
}
#ifdef FASTIO
// wt, off
void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }
void read_graph(int M, bool wt = false, int off = 1) {
for (int m = 0; m < M; ++m) {
INT(a, b);
a -= off, b -= off;
if (!wt) {
add(a, b);
} else {
T c;
read(c);
add(a, b, c);
}
}
build();
}
#endif
void build() {
assert(!prepared);
prepared = true;
indptr.assign(N + 1, 0);
for (auto&& e : edges) {
indptr[e.frm + 1]++;
if (!directed) indptr[e.to + 1]++;
}
for (int v = 0; v < N; ++v) {
indptr[v + 1] += indptr[v];
}
auto counter = indptr;
csr_edges.resize(indptr.back() + 1);
for (auto&& e : edges) {
csr_edges[counter[e.frm]++] = e;
if (!directed)
csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
}
}
OutgoingEdges operator[](int v) const {
assert(prepared);
return {this, indptr[v], indptr[v + 1]};
}
vc<int> deg_array() const {
if (vc_deg.empty()) calc_deg();
return vc_deg;
}
pair<vc<int>, vc<int>> deg_array_inout() const {
if (vc_indeg.empty()) calc_deg_inout();
return {vc_indeg, vc_outdeg};
}
int deg(int v) const {
if (vc_deg.empty()) calc_deg();
return vc_deg[v];
}
int in_deg(int v) const {
if (vc_indeg.empty()) calc_deg_inout();
return vc_indeg[v];
}
int out_deg(int v) const {
if (vc_outdeg.empty()) calc_deg_inout();
return vc_outdeg[v];
}
#ifdef FASTIO
void debug() {
#ifdef LOCAL
print("Graph");
if (!prepared) {
print("frm to cost id");
for (auto&& e : edges) print(e.frm, e.to, e.cost, e.id);
} else {
print("indptr", indptr);
print("frm to cost id");
FOR(v, N) for (auto&& e : (*this)[v]) print(e.frm, e.to, e.cost, e.id);
}
flush();
#endif
}
#endif
vc<int> new_idx;
vc<bool> used_e;
// G における頂点 V[i] が、新しいグラフで i になるようにする
// {G, es}
// sum(deg(v)) の計算量になっていて、
// 新しいグラフの n+m より大きい可能性があるので注意
Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
if (len(new_idx) != N) new_idx.assign(N, -1);
int n = len(V);
FOR(i, n) new_idx[V[i]] = i;
Graph<T, directed> G(n);
vc<int> history;
FOR(i, n) {
for (auto&& e : (*this)[V[i]]) {
if (len(used_e) <= e.id) used_e.resize(e.id + 1);
if (used_e[e.id]) continue;
int a = e.frm, b = e.to;
if (new_idx[a] != -1 && new_idx[b] != -1) {
history.eb(e.id);
used_e[e.id] = 1;
int eid = (keep_eid ? e.id : -1);
G.add(new_idx[a], new_idx[b], e.cost, eid);
}
}
}
FOR(i, n) new_idx[V[i]] = -1;
for (auto&& eid : history) used_e[eid] = 0;
G.build();
return G;
}
Graph<T, true> to_directed_tree(int root = -1) const {
if (root == -1) root = 0;
assert(!is_directed && prepared && M == N - 1);
Graph<T, true> G1(N);
vc<int> par(N, -1);
auto dfs = [&](auto& dfs, int v) -> void {
for (auto& e : (*this)[v]) {
if (e.to == par[v]) continue;
par[e.to] = v, dfs(dfs, e.to);
}
};
dfs(dfs, root);
for (auto& e : edges) {
int a = e.frm, b = e.to;
if (par[a] == b) swap(a, b);
assert(par[b] == a);
G1.add(a, b, e.cost);
}
G1.build();
return G1;
}
int get_eid(u64 a, u64 b) const {
if (len(MP_FOR_EID) == 0) {
MP_FOR_EID.build(N - 1);
for (auto& e : edges) {
u64 a = e.frm, b = e.to;
u64 k = to_eid_key(a, b);
MP_FOR_EID[k] = e.id;
}
}
return MP_FOR_EID.get(to_eid_key(a, b), -1);
}
u64 to_eid_key(u64 a, u64 b) const {
if (!directed && a > b) swap(a, b);
return N * a + b;
}
private:
void calc_deg() const {
assert(vc_deg.empty());
vc_deg.resize(N);
for (auto&& e : edges) vc_deg[e.frm]++, vc_deg[e.to]++;
}
void calc_deg_inout() const {
assert(vc_indeg.empty());
vc_indeg.resize(N);
vc_outdeg.resize(N);
for (auto&& e : edges) {
vc_indeg[e.to]++, vc_outdeg[e.frm]++;
}
}
};
#line 3 "graph/tree.hpp"
// HLD euler tour をとっていろいろ
// HLD=false: 入力辺順で preorder
template <typename GT, bool HLD = true>
struct Tree {
using Graph_type = GT;
using WT = typename GT::cost_type;
int N = 0;
vector<int> LID, RID, head, V, parent, VtoE, EtoV;
vc<int> depth;
vc<WT> depth_weighted;
vc<int> memo_tail;
Tree() = default;
Tree(const GT &G, int r = 0) { build(G, r); }
void build(const GT &G, int r = 0) {
N = G.N;
assert(G.is_prepared());
assert(G.M == N - 1);
FOR(i, N - 1) assert(G.edges[i].id == i);
assert(0 <= r && r < N);
if constexpr (!HLD)
build_simple(G, r);
else
build_HLD(G, r);
}
vc<int> heavy_path_at(int v) const {
static_assert(HLD);
assert(head[v] == v);
int k = LID[v];
vc<int> P;
while (k < N && head[V[k]] == v) P.eb(V[k++]);
return P;
}
int heavy_child(int v) const {
static_assert(HLD);
if (RID[v] == LID[v] + 1) return -1;
return V[LID[v] + 1];
}
int tail(int v) {
static_assert(HLD);
if (memo_tail.empty()) {
memo_tail.assign(N, -1);
FOR_R(i, N) {
int v = V[i];
int w = heavy_child(v);
memo_tail[v] = (w == -1 ? v : memo_tail[w]);
}
}
return memo_tail[v];
}
int e_to_v(int eid) const { return EtoV[eid]; }
int v_to_e(int v) const { return VtoE[v]; }
int get_eid(int u, int v) const {
if (parent[u] != v) swap(u, v);
assert(parent[u] == v);
return VtoE[u];
}
int ELID(int v) const { return 2 * LID[v] - depth[v]; }
int ERID(int v) const { return 2 * RID[v] - depth[v] - 1; }
// 目標地点へ進む個数が k
int LA(int v, int k) const {
static_assert(HLD);
assert(k <= depth[v]);
while (1) {
int u = head[v];
if (LID[v] - k >= LID[u]) return V[LID[v] - k];
k -= LID[v] - LID[u] + 1;
v = parent[u];
}
}
int LCA(int u, int v) const {
static_assert(HLD);
for (;; v = parent[head[v]]) {
if (LID[u] > LID[v]) swap(u, v);
if (head[u] == head[v]) return u;
}
}
int meet(int a, int b, int c) const {
static_assert(HLD);
return LCA(a, b) ^ LCA(a, c) ^ LCA(b, c);
}
int subtree_size(int v) const { return RID[v] - LID[v]; }
int subtree_size(int v, int root) const {
static_assert(HLD);
if (v == root) return N;
int x = jump(v, root, 1);
if (in_subtree(v, x)) return RID[v] - LID[v];
return N - RID[x] + LID[x];
}
int dist(int a, int b) const {
static_assert(HLD);
int c = LCA(a, b);
return depth[a] + depth[b] - 2 * depth[c];
}
WT dist_weighted(int a, int b) const {
static_assert(HLD);
int c = LCA(a, b);
return depth_weighted[a] + depth_weighted[b] - WT(2) * depth_weighted[c];
}
// a is in b
bool in_subtree(int a, int b) const {
return LID[b] <= LID[a] && LID[a] < RID[b];
}
int jump(int a, int b, ll k) const {
static_assert(HLD);
if (k == 1) {
if (a == b) return -1;
return (in_subtree(b, a) ? LA(b, depth[b] - depth[a] - 1) : parent[a]);
}
int c = LCA(a, b);
int d_ac = depth[a] - depth[c];
int d_bc = depth[b] - depth[c];
if (k > d_ac + d_bc) return -1;
if (k <= d_ac) return LA(a, k);
return LA(b, d_ac + d_bc - k);
}
vc<int> collect_child(int v) const {
vc<int> res;
for (int k = LID[v] + 1; k < RID[v];) {
res.eb(V[k]), k = RID[V[k]];
}
return res;
}
vc<int> collect_subtree(int v) const {
return {V.begin() + LID[v], V.begin() + RID[v]};
}
vc<int> collect_light(int v) const {
static_assert(HLD);
vc<int> res;
for (int k = LID[v] + 1; k < RID[v];) {
if (head[V[k]] == V[k]) res.eb(V[k]);
k = RID[V[k]];
}
return res;
}
vc<pair<int, int>> get_path_decomposition(int u, int v, bool edge) const {
static_assert(HLD);
// [始点, 終点] の"閉"区間列。
vc<pair<int, int>> up, down;
while (1) {
if (head[u] == head[v]) break;
if (LID[u] < LID[v]) {
down.eb(LID[head[v]], LID[v]);
v = parent[head[v]];
} else {
up.eb(LID[u], LID[head[u]]);
u = parent[head[u]];
}
}
if (LID[u] < LID[v]) down.eb(LID[u] + edge, LID[v]);
elif (LID[v] + edge <= LID[u]) up.eb(LID[u], LID[v] + edge);
reverse(all(down));
up.insert(up.end(), all(down));
return up;
}
// 辺の列の情報 (frm,to,str)
// str = "heavy_up", "heavy_down", "light_up", "light_down"
vc<tuple<int, int, string>> get_path_decomposition_detail(
int u, int v) const {
static_assert(HLD);
vc<tuple<int, int, string>> up, down;
while (1) {
if (head[u] == head[v]) break;
if (LID[u] < LID[v]) {
if (v != head[v]) down.eb(head[v], v, "heavy_down"), v = head[v];
down.eb(parent[v], v, "light_down"), v = parent[v];
} else {
if (u != head[u]) up.eb(u, head[u], "heavy_up"), u = head[u];
up.eb(u, parent[u], "light_up"), u = parent[u];
}
}
if (LID[u] < LID[v]) down.eb(u, v, "heavy_down");
elif (LID[v] < LID[u]) up.eb(u, v, "heavy_up");
reverse(all(down));
concat(up, down);
return up;
}
vc<int> restore_path(int u, int v) const {
vc<int> L, R;
while (depth[u] > depth[v]) L.eb(u), u = parent[u];
while (depth[u] < depth[v]) R.eb(v), v = parent[v];
while (u != v) L.eb(u), R.eb(v), u = parent[u], v = parent[v];
L.eb(u);
while (len(R)) L.eb(POP(R));
return L;
}
// path [a,b] と [c,d] の交わり. 空ならば {-1,-1}.
// https://codeforces.com/problemset/problem/500/G
pair<int, int> path_intersection(int a, int b, int c, int d) const {
static_assert(HLD);
int ab = LCA(a, b), ac = LCA(a, c), ad = LCA(a, d);
int bc = LCA(b, c), bd = LCA(b, d), cd = LCA(c, d);
int x = ab ^ ac ^ bc, y = ab ^ ad ^ bd; // meet(a,b,c), meet(a,b,d)
if (x != y) return {x, y};
int z = ac ^ ad ^ cd;
if (x != z) x = -1;
return {x, x};
}
// uv path 上で check(v) を満たす最後の v
// なければ （つまり check(v) が ng ）-1
template <class F>
int max_path(F check, int u, int v) const {
static_assert(HLD);
if (!check(u)) return -1;
auto pd = get_path_decomposition(u, v, false);
for (auto [a, b] : pd) {
if (!check(V[a])) return u;
if (check(V[b])) {
u = V[b];
continue;
}
int c =
binary_search([&](int c) -> bool { return check(V[c]); }, a, b, 0);
return V[c];
}
return u;
}
private:
void build_simple(const GT &G, int r = 0) {
N = G.N;
LID.assign(N, 0), RID.assign(N, 0);
V.assign(N, -1), parent.assign(N, -1), VtoE.assign(N, -1),
EtoV.assign(N - 1, -1);
depth.assign(N, 0), depth_weighted.assign(N, 0);
// 1st dfs.
int k = 0;
vc<int> st;
st.reserve(N);
st.eb(r);
while (len(st)) {
int v = POP(st);
LID[v] = k, V[k] = v;
++k;
for (int i = G.indptr[v + 1] - 1; i >= G.indptr[v]; --i) {
auto &e = G.csr_edges[i];
if (e.to == parent[v]) continue;
parent[e.to] = v;
depth[e.to] = depth[v] + 1;
depth_weighted[e.to] = depth_weighted[v] + e.cost;
VtoE[e.to] = e.id, EtoV[e.id] = e.to;
st.eb(e.to);
}
}
FOR_R(i, N) {
int v = V[i];
chmax(RID[v], LID[v] + 1);
if (parent[v] != -1) chmax(RID[parent[v]], RID[v]);
}
}
void build_HLD(const GT &G, int r = 0) {
N = G.N;
LID.assign(N, 0), RID.assign(N, 0), head.assign(N, r);
V.assign(N, -1), parent.assign(N, -1), VtoE.assign(N, -1),
EtoV.assign(N - 1, -1);
depth.assign(N, 0), depth_weighted.assign(N, 0);
memo_tail.clear();
// 1st dfs.
{
int k = 0;
vc<int> st;
st.reserve(N);
st.eb(r);
while (len(st)) {
int v = POP(st);
V[k++] = v;
for (auto &e : G[v]) {
if (e.to == parent[v]) continue;
parent[e.to] = v, st.eb(e.to), depth[e.to] = depth[v] + 1;
depth_weighted[e.to] = depth_weighted[v] + e.cost;
VtoE[e.to] = e.id, EtoV[e.id] = e.to;
}
}
// 一時的に RID[v] := sz[v]
FOR_R(i, N) {
int v = V[i];
RID[v] += 1;
if (parent[v] != -1) RID[parent[v]] += RID[v];
}
}
// 2nd dfs.
{
int k = 0;
vc<int> st;
st.reserve(N);
st.eb(r);
while (len(st)) {
int v = POP(st);
V[k] = v, LID[v] = k;
RID[v] = k + RID[v];
++k;
int max_sz = 0, max_ch = -1;
for (auto &e : G[v]) {
if (e.to == parent[v]) continue;
if (chmax(max_sz, RID[e.to])) max_ch = e.to;
}
for (int i = G.indptr[v + 1] - 1; i >= G.indptr[v]; --i) {
auto &e = G.csr_edges[i];
if (e.to == parent[v] || e.to == max_ch) continue;
st.eb(e.to), head[e.to] = e.to;
}
if (max_ch != -1) st.eb(max_ch), head[max_ch] = head[v];
}
}
}
};
#line 1 "ds/unionfind/unionfind.hpp"
struct UnionFind {
int n, n_comp;
vc<int> dat; // par or (-size)
UnionFind(int n = 0) { build(n); }
void build(int m) {
n = m, n_comp = m;
dat.assign(n, -1);
}
void reset() { build(n); }
int operator[](int x) {
while (dat[x] >= 0) {
int pp = dat[dat[x]];
if (pp < 0) { return dat[x]; }
x = dat[x] = pp;
}
return x;
}
ll size(int x) {
x = (*this)[x];
return -dat[x];
}
bool merge(int x, int y) {
x = (*this)[x], y = (*this)[y];
if (x == y) return false;
if (-dat[x] < -dat[y]) swap(x, y);
dat[x] += dat[y], dat[y] = x, n_comp--;
return true;
}
vc<int> get_all() {
vc<int> A(n);
FOR(i, n) A[i] = (*this)[i];
return A;
}
};
#line 11 "test/3_yukicoder/1600_2.test.cpp"
#line 1 "mod/modint_common.hpp"
#line 1 "other/bit.hpp"
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T kth_bit(int k) {
assert(0 <= k && k < int(8 * sizeof(T)));
return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
assert(0 <= k && k < int(8 * sizeof(T)));
return x >> k & 1;
}
template <typename UINT>
struct all_bit {
static_assert(is_unsigned<UINT>::value);
UINT s;
all_bit(UINT s) : s(s) {}
struct iter {
UINT s;
int operator*() const { return lowbit(s); }
void operator++() { s &= s - 1; }
bool operator!=(nullptr_t) const { return s; }
};
iter begin() const { return {s}; }
nullptr_t end() const { return nullptr; }
};
template <typename UINT>
struct all_subset {
static_assert(is_unsigned<UINT>::value);
UINT s;
all_subset(UINT s) : s(s) {}
struct iter {
UINT s, t;
bool done = false;
UINT operator*() const { return t; }
void operator++() {
done = (t == 0);
t = (t - 1) & s;
}
bool operator!=(nullptr_t) const { return !done; }
};
iter begin() const { return {s, s}; }
nullptr_t end() const { return nullptr; }
};
constexpr u64 full_mask(int n) {
assert(0 <= n && n <= 64);
return n == 64 ? -1ULL : (1ULL << n) - 1;
}
u64 bit_reverse(u64 x) {
x = ((x & 0x5555555555555555ULL) << 1) | ((x >> 1) & 0x5555555555555555ULL);
x = ((x & 0x3333333333333333ULL) << 2) | ((x >> 2) & 0x3333333333333333ULL);
x = ((x & 0x0f0f0f0f0f0f0f0fULL) << 4) | ((x >> 4) & 0x0f0f0f0f0f0f0f0fULL);
x = ((x & 0x00ff00ff00ff00ffULL) << 8) | ((x >> 8) & 0x00ff00ff00ff00ffULL);
x = ((x & 0x0000ffff0000ffffULL) << 16) | ((x >> 16) & 0x0000ffff0000ffffULL);
x = (x << 32) | (x >> 32);
return x;
}
#line 3 "mod/modint_common.hpp"
struct has_mod_impl {
template <class T>
static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};
template <typename mint>
mint fact(int n) {
static vector<mint> dat = {1, 1};
static int mod = 0;
if (mod != mint::get_mod()) {
mod = mint::get_mod();
dat = {1, 1};
}
assert(0 <= n && n < mod);
if (len(dat) <= n) {
int now = len(dat);
int m = min(mod, 1 << (topbit(n) + 1));
dat.resize(m);
FOR(i, now, m) dat[i] = dat[i - 1] * mint::raw(i);
}
return dat[n];
}
template <typename mint>
mint fact_inv(int n) {
if (n < 0) return mint(0);
static vector<mint> dat = {1, 1};
static int mod = 0;
if (mod != mint::get_mod()) {
mod = mint::get_mod();
dat = {1, 1};
}
assert(0 <= n && n < mod);
if (len(dat) <= n) {
int now = len(dat);
int m = min(mod, 1 << (topbit(n) + 1));
dat.resize(m);
dat[m - 1] = fact<mint>(m - 1).inverse();
FOR_R(i, now, m - 1) dat[i] = dat[i + 1] * mint::raw(i + 1);
}
return dat[n];
}
template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
return (mint(1) * ... * fact_inv<mint>(xs));
}
template <typename mint>
mint inv(int n) {
return fact<mint>(n - 1) * fact_inv<mint>(n);
}
template <>
double inv<double>(int n) {
assert(n != 0);
return 1.0 / n;
}
template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&...tail) {
return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}
template <typename mint>
mint C_dense(int n, int k) {
assert(n >= 0);
if (k < 0 || n < k) return 0;
static vvc<mint> C;
static int H = 0, W = 0;
static int mod = 0;
if (mod != mint::get_mod()) {
mod = mint::get_mod();
C.clear();
H = W = 0;
}
auto calc = [&](int i, int j) -> mint {
if (i == 0) return (j == 0 ? mint(1) : mint(0));
return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
};
if (W <= k) {
FOR(i, H) {
C[i].resize(k + 1);
FOR(j, W, k + 1) { C[i][j] = calc(i, j); }
}
W = k + 1;
}
if (H <= n) {
C.resize(n + 1);
FOR(i, H, n + 1) {
C[i].resize(W);
FOR(j, W) { C[i][j] = calc(i, j); }
}
H = n + 1;
}
return C[n][k];
}
template <typename mint, bool large = false, bool dense = false>
mint C(ll n, ll k) {
assert(n >= 0);
if (k < 0 || n < k) return 0;
if constexpr (dense) return C_dense<mint>(n, k);
if constexpr (!large) return multinomial<mint>(n, k, n - k);
k = min(k, n - k);
mint x(1);
FOR(i, k) x *= mint(n - i);
return x * fact_inv<mint>(k);
}
template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
assert(n >= 0);
assert(0 <= k && k <= n);
if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
return mint(1) / C<mint, 1>(n, k);
}
// [x^d](1-x)^{-n}
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
assert(n >= 0);
if (d < 0) return mint(0);
if (n == 0) {
return (d == 0 ? mint(1) : mint(0));
}
return C<mint, large, dense>(n + d - 1, d);
}
#line 2 "mod/modint.hpp"
template <int mod>
struct modint {
static constexpr u32 umod = u32(mod);
static_assert(0 < umod && umod < u32(1) << 31);
u32 val;
static modint raw(u32 v) {
modint x;
x.val = v;
return x;
}
constexpr modint() : val(0) {}
constexpr modint(u32 x) : val(x % umod) {}
constexpr modint(u64 x) : val(x % umod) {}
constexpr modint(u128 x) : val(x % umod) {}
constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){};
constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){};
constexpr modint(i128 x) : val((x %= mod) < 0 ? x + mod : x){};
bool operator<(const modint &other) const { return val < other.val; }
modint &operator+=(const modint &p) {
if ((val += p.val) >= umod) val -= umod;
return *this;
}
modint &operator-=(const modint &p) {
if ((val += umod - p.val) >= umod) val -= umod;
return *this;
}
modint &operator*=(const modint &p) {
val = u64(val) * p.val % umod;
return *this;
}
modint &operator/=(const modint &p) {
*this *= p.inverse();
return *this;
}
modint operator-() const { return modint::raw(val ? mod - val : u32(0)); }
modint operator+(const modint &p) const { return modint(*this) += p; }
modint operator-(const modint &p) const { return modint(*this) -= p; }
modint operator*(const modint &p) const { return modint(*this) *= p; }
modint operator/(const modint &p) const { return modint(*this) /= p; }
bool operator==(const modint &p) const { return val == p.val; }
bool operator!=(const modint &p) const { return val != p.val; }
modint inverse() const {
int a = val, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
return modint(u);
}
modint pow(ll n) const {
if (n < 0) return inverse().pow(-n);
assert(n >= 0);
modint ret(1), mul(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
static constexpr int get_mod() { return mod; }
// (n, r), r は 1 の 2^n 乗根
static constexpr pair<int, int> ntt_info() {
if (mod == 120586241) return {20, 74066978};
if (mod == 167772161) return {25, 17};
if (mod == 469762049) return {26, 30};
if (mod == 754974721) return {24, 362};
if (mod == 880803841) return {23, 211};
if (mod == 943718401) return {22, 663003469};
if (mod == 998244353) return {23, 31};
if (mod == 1004535809) return {21, 582313106};
if (mod == 1012924417) return {21, 368093570};
if (mod == 1224736769) return {24, 1191450770};
if (mod == 2013265921) return {27, 244035102};
return {-1, -1};
}
static constexpr bool can_ntt() { return ntt_info().fi != -1; }
};
#ifdef FASTIO
template <int mod>
void rd(modint<mod> &x) {
fastio::rd(x.val);
x.val %= mod;
// assert(0 <= x.val && x.val < mod);
}
template <int mod>
void wt(modint<mod> x) {
fastio::wt(x.val);
}
#endif
using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
#line 13 "test/3_yukicoder/1600_2.test.cpp"
using mint = modint107;
void solve() {
LL(N, M);
Graph<mint, 0> G(N);
UnionFind uf(N);
vc<pair<int, int>> edges;
vc<bool> in_G(M);
mint wt = 1;
FOR(i, M) {
LL(a, b);
--a, --b;
edges.eb(a, b);
wt += wt;
if (uf.merge(a, b)) {
in_G[i] = 1;
G.add(a, b, wt);
}
}
G.build();
Tree<decltype(G)> tree(G);
auto& par = tree.parent;
vc<int> X, Y, W;
FOR(e, M) {
if (in_G[e]) continue;
auto [a, b] = edges[e];
a = tree.LID[a], b = tree.LID[b];
if (a > b) swap(a, b);
X.eb(a), Y.eb(b), W.eb(e);
}
using Mono = Monoid_Min<int>;
using ST = Sparse_Table<Mono>;
Wavelet_Matrix_2D_Range<int, false, false, Static_Range_Product<Mono, ST>>
seg(len(X),
[&](int i) -> tuple<int, int, int> { return {X[i], Y[i], W[i]}; });
LL(Q);
FOR(Q) {
LL(u, v, idx);
--u, --v, --idx;
auto [x, y] = edges[idx];
if (par[y] == x) swap(x, y);
bool in_u = tree.in_subtree(u, x);
bool in_v = tree.in_subtree(v, x);
if (!in_G[idx] || in_u == in_v) {
print(tree.dist_weighted(u, v));
continue;
}
// 木の外に出る移動が必要
int l = tree.LID[x], r = tree.RID[x];
int min_i = Mono::op(seg.prod(0, l, l, r), seg.prod(l, r, r, N));
if (min_i == Mono::id()) {
print(-1);
continue;
}
auto [p, q] = edges[min_i];
bool in_p = tree.in_subtree(p, x);
if (!in_u) swap(u, v);
if (!in_p) swap(p, q);
mint ANS = tree.dist_weighted(u, p) + tree.dist_weighted(v, q);
ANS += mint(2).pow(min_i + 1);
print(ANS);
}
}
signed main() {
solve();
return 0;
}