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test/1_mytest/mo_on_tree.test.cpp
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- Last update: 2025-01-27 19:24:29+09:00
- Problem: https://judge.yosupo.jp/problem/aplusb
Depends on
- alg/monoid/add_pair.hpp
- alg/monoid/affine.hpp
- alg/monoid/monoid_reverse.hpp
ds/hashmap.hpp
- ds/offline_query/mo.hpp
- ds/segtree/segtree.hpp
- graph/base.hpp
- graph/ds/mo_on_tree.hpp
- graph/ds/tree_monoid.hpp
- graph/tree.hpp
- mod/modint.hpp
- mod/modint_common.hpp
- my_template.hpp
- random/base.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
#include "random/base.hpp"
#include "graph/tree.hpp"
#include "graph/ds/mo_on_tree.hpp"
#include "graph/ds/tree_monoid.hpp"
#include "alg/monoid/affine.hpp"
#include "alg/monoid/add_pair.hpp"
#include "mod/modint.hpp"
using mint = modint998;
using AFF = pair<mint, mint>;
AFF gen() {
mint a = RNG(1, 3);
mint b = RNG(0, 3);
return {a, b};
}
template <typename Mono, bool EDGE>
void test() {
constexpr bool ORIENTED = !(Mono::commute);
FOR(N, 1, 50) {
FOR(Q, 1, 50) {
vc<pi> query(Q);
vc<AFF> dat;
if (!EDGE) {
FOR(v, N) dat.eb(gen());
} else {
FOR(i, N - 1) dat.eb(gen());
}
Graph<int, 0> G(N);
FOR(v, 1, N) {
int p = RNG(0, v);
G.add(p, v);
}
G.build();
Tree<decltype(G)> tree(G);
Tree_Monoid<decltype(tree), Mono, EDGE> TM(tree, dat);
FOR(q, Q) {
int a = RNG(0, N);
int b = RNG(0, N);
query[q] = {a, b};
}
Mo_on_Tree<decltype(tree), ORIENTED> mo(tree);
for (auto&& [a, b]: query) mo.add(a, b);
if constexpr (!EDGE) {
AFF f = Mono::unit();
auto init = [&]() -> void { f = dat[0]; };
auto add_l = [&](int v) -> void { f = Mono::op(dat[v], f); };
auto rm_l = [&](int v) -> void { f = Mono::op(Mono::inverse(dat[v]), f); };
auto add_r = [&](int v) -> void { f = Mono::op(f, dat[v]); };
auto rm_r = [&](int v) -> void { f = Mono::op(f, Mono::inverse(dat[v])); };
auto ans = [&](int q) -> void { assert(f == TM.prod_path(query[q].fi, query[q].se)); };
mo.calc_vertex(init, add_l, add_r, rm_l, rm_r, ans);
} else {
AFF f = Mono::unit();
auto get = [&](int a, int b) -> int { return tree.v_to_e((tree.parent[a] == b ? a : b)); };
auto init = [&]() -> void {};
auto add_l = [&](int a, int b) -> void { f = Mono::op(dat[get(a, b)], f); };
auto rm_l = [&](int a, int b) -> void { f = Mono::op(Mono::inverse(dat[get(a, b)]), f); };
auto add_r = [&](int a, int b) -> void { f = Mono::op(f, dat[get(a, b)]); };
auto rm_r = [&](int a, int b) -> void { f = Mono::op(f, Mono::inverse(dat[get(a, b)])); };
auto ans = [&](int q) -> void { assert(f == TM.prod_path(query[q].fi, query[q].se)); };
mo.calc_edge(init, add_l, add_r, rm_l, rm_r, ans);
}
}
}
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
// パスの向きが可逆で頂点可換モノイド積
test<Monoid_Add_Pair<mint>, false>();
// パスの向きが不可逆で頂点非可換モノイド積
test<Monoid_Affine<mint>, false>();
// パスの向きが可逆で辺可換モノイド積
test<Monoid_Add_Pair<mint>, true>();
// パスの向きが不可逆で辺非可換モノイド積
test<Monoid_Affine<mint>, true>();
solve();
return 0;
}#line 1 "test/1_mytest/mo_on_tree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
// https://codeforces.com/blog/entry/96344
// https://codeforces.com/blog/entry/126772?#comment-1154880
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,popcnt")
#include <bits/stdc++.h>
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 T>
constexpr T infty = 0;
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<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
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 vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = 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 FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, 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
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) {
return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
return x >> k & 1;
}
template <typename UINT>
struct all_bit {
struct iter {
UINT s;
iter(UINT s) : s(s) {}
int operator*() const { return lowbit(s); }
iter &operator++() {
s &= s - 1;
return *this;
}
bool operator!=(const iter) const { return s != 0; }
};
UINT s;
all_bit(UINT s) : s(s) {}
iter begin() const { return iter(s); }
iter end() const { return iter(0); }
};
template <typename UINT>
struct all_subset {
static_assert(is_unsigned<UINT>::value);
struct iter {
UINT s, t;
bool ed;
iter(UINT s) : s(s), t(s), ed(0) {}
int operator*() const { return s ^ t; }
iter &operator++() {
(t == 0 ? ed = 1 : t = (t - 1) & s);
return *this;
}
bool operator!=(const iter) const { return !ed; }
};
UINT s;
all_subset(UINT s) : s(s) {}
iter begin() const { return iter(s); }
iter end() const { return iter(0); }
};
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sm = 0;
for (auto &&a: A) sm += a;
return sm;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &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>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(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) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? 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>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<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>
vector<int> argsort(const vector<T> &A) {
vector<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) {
vc<T> &res = first;
(res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 3 "test/1_mytest/mo_on_tree.test.cpp"
#line 2 "random/base.hpp"
u64 RNG_64() {
static u64 x_ = u64(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL;
x_ ^= x_ << 7;
return x_ ^= x_ >> 9;
}
u64 RNG(u64 lim) { return RNG_64() % lim; }
ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 2 "graph/tree.hpp"
#line 2 "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) {
if (cap == 0) extend();
int i = index(k);
if (!used[i]) { 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 3 "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;
vc<int> vc_deg, vc_indeg, vc_outdeg;
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() { 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();
}
void add(int frm, int to, T cost = 1, int i = -1) {
assert(!prepared);
assert(0 <= frm && 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() {
if (vc_deg.empty()) calc_deg();
return vc_deg;
}
pair<vc<int>, vc<int>> deg_array_inout() {
if (vc_indeg.empty()) calc_deg_inout();
return {vc_indeg, vc_outdeg};
}
int deg(int v) {
if (vc_deg.empty()) calc_deg();
return vc_deg[v];
}
int in_deg(int v) {
if (vc_indeg.empty()) calc_deg_inout();
return vc_indeg[v];
}
int out_deg(int v) {
if (vc_outdeg.empty()) calc_deg_inout();
return vc_outdeg[v];
}
#ifdef FASTIO
void debug() {
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);
}
}
#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) {
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;
}
HashMap<int> MP_FOR_EID;
int get_eid(u64 a, u64 b) {
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) {
if (!directed && a > b) swap(a, b);
return N * a + b;
}
private:
void calc_deg() {
assert(vc_deg.empty());
vc_deg.resize(N);
for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
}
void calc_deg_inout() {
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 4 "graph/tree.hpp"
// HLD euler tour をとっていろいろ。
template <typename GT>
struct Tree {
using Graph_type = GT;
GT &G;
using WT = typename GT::cost_type;
int N;
vector<int> LID, RID, head, V, parent, VtoE;
vc<int> depth;
vc<WT> depth_weighted;
Tree(GT &G, int r = 0, bool hld = 1) : G(G) { build(r, hld); }
void build(int r = 0, bool hld = 1) {
if (r == -1) return; // build を遅延したいとき
N = G.N;
LID.assign(N, -1), RID.assign(N, -1), head.assign(N, r);
V.assign(N, -1), parent.assign(N, -1), VtoE.assign(N, -1);
depth.assign(N, -1), depth_weighted.assign(N, 0);
assert(G.is_prepared());
int t1 = 0;
dfs_sz(r, -1, hld);
dfs_hld(r, t1);
}
void dfs_sz(int v, int p, bool hld) {
auto &sz = RID;
parent[v] = p;
depth[v] = (p == -1 ? 0 : depth[p] + 1);
sz[v] = 1;
int l = G.indptr[v], r = G.indptr[v + 1];
auto &csr = G.csr_edges;
// 使う辺があれば先頭にする
for (int i = r - 2; i >= l; --i) {
if (hld && depth[csr[i + 1].to] == -1) swap(csr[i], csr[i + 1]);
}
int hld_sz = 0;
for (int i = l; i < r; ++i) {
auto e = csr[i];
if (depth[e.to] != -1) continue;
depth_weighted[e.to] = depth_weighted[v] + e.cost;
VtoE[e.to] = e.id;
dfs_sz(e.to, v, hld);
sz[v] += sz[e.to];
if (hld && chmax(hld_sz, sz[e.to]) && l < i) { swap(csr[l], csr[i]); }
}
}
void dfs_hld(int v, int ×) {
LID[v] = times++;
RID[v] += LID[v];
V[LID[v]] = v;
bool heavy = true;
for (auto &&e: G[v]) {
if (depth[e.to] <= depth[v]) continue;
head[e.to] = (heavy ? head[v] : e.to);
heavy = false;
dfs_hld(e.to, times);
}
}
vc<int> heavy_path_at(int v) {
vc<int> P = {v};
while (1) {
int a = P.back();
for (auto &&e: G[a]) {
if (e.to != parent[a] && head[e.to] == v) {
P.eb(e.to);
break;
}
}
if (P.back() == a) break;
}
return P;
}
int heavy_child(int v) {
int k = LID[v] + 1;
if (k == N) return -1;
int w = V[k];
return (parent[w] == v ? w : -1);
}
int e_to_v(int eid) {
auto e = G.edges[eid];
return (parent[e.frm] == e.to ? e.frm : e.to);
}
int v_to_e(int v) { return VtoE[v]; }
int get_eid(int u, int v) {
if (parent[u] != v) swap(u, v);
assert(parent[u] == v);
return VtoE[u];
}
int ELID(int v) { return 2 * LID[v] - depth[v]; }
int ERID(int v) { return 2 * RID[v] - depth[v] - 1; }
// 目標地点へ進む個数が k
int LA(int v, int k) {
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 la(int u, int v) { return LA(u, v); }
int LCA(int u, int v) {
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) { return LCA(a, b) ^ LCA(a, c) ^ LCA(b, c); }
int lca(int u, int v) { return LCA(u, v); }
int subtree_size(int v, int root = -1) {
if (root == -1) return RID[v] - LID[v];
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) {
int c = LCA(a, b);
return depth[a] + depth[b] - 2 * depth[c];
}
WT dist_weighted(int a, int b) {
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) { return LID[b] <= LID[a] && LID[a] < RID[b]; }
int jump(int a, int b, ll k) {
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) {
vc<int> res;
for (auto &&e: G[v])
if (e.to != parent[v]) res.eb(e.to);
return res;
}
vc<int> collect_light(int v) {
vc<int> res;
bool skip = true;
for (auto &&e: G[v])
if (e.to != parent[v]) {
if (!skip) res.eb(e.to);
skip = false;
}
return res;
}
vc<pair<int, int>> get_path_decomposition(int u, int v, bool edge) {
// [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) {
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) {
vc<int> P;
for (auto &&[a, b]: get_path_decomposition(u, v, 0)) {
if (a <= b) {
FOR(i, a, b + 1) P.eb(V[i]);
} else {
FOR_R(i, b, a + 1) P.eb(V[i]);
}
}
return P;
}
// 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) {
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) {
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;
}
};
#line 1 "ds/offline_query/mo.hpp"
// Nsqrt(Q)
struct Mo {
vc<pair<int, int>> LR;
void add(int L, int R) { LR.emplace_back(L, R); }
static vc<int> get_mo_order(vc<pair<int, int>> LR) {
int N = 1;
for (auto &&[l, r]: LR) chmax(N, l), chmax(N, r);
int Q = len(LR);
if (Q == 0) return {};
int bs = sqrt(3) * N / sqrt(2 * Q);
chmax(bs, 1);
vc<int> I(Q);
iota(all(I), 0);
sort(all(I), [&](int a, int b) {
int aa = LR[a].fi / bs, bb = LR[b].fi / bs;
if (aa != bb) return aa < bb;
return (aa & 1) ? LR[a].se > LR[b].se : LR[a].se < LR[b].se;
});
auto cost = [&](int a, int b) -> int {
return abs(LR[I[a]].fi - LR[I[b]].fi) + abs(LR[I[a]].se - LR[I[b]].se);
};
// ランダムケースで数パーセント
FOR(k, Q - 5) {
if (cost(k, k + 2) + cost(k + 1, k + 3)
< cost(k, k + 1) + cost(k + 2, k + 3)) {
swap(I[k + 1], I[k + 2]);
}
if (cost(k, k + 3) + cost(k + 1, k + 4)
< cost(k, k + 1) + cost(k + 3, k + 4)) {
swap(I[k + 1], I[k + 3]);
}
}
return I;
}
template <typename F1, typename F2, typename F3, typename F4, typename F5>
void calc(F1 add_l, F2 add_r, F3 rm_l, F4 rm_r, F5 query) {
auto I = get_mo_order(LR);
int l = 0, r = 0;
for (auto idx: I) {
while (l > LR[idx].fi) add_l(--l);
while (r < LR[idx].se) add_r(r++);
while (l < LR[idx].fi) rm_l(l++);
while (r > LR[idx].se) rm_r(--r);
query(idx);
}
}
};
#line 3 "graph/ds/mo_on_tree.hpp"
// https://codeforces.com/contest/852/problem/I
template <typename TREE, bool ORIENTED = false>
struct Mo_on_Tree {
TREE& tree;
vc<pair<int, int>> LR;
Mo mo;
Mo_on_Tree(TREE& tree) : tree(tree) {}
void add(int u, int v) {
if constexpr (!ORIENTED) {
if (tree.LID[u] > tree.LID[v]) swap(u, v);
}
LR.eb(tree.ELID(u) + 1, tree.ELID(v) + 1);
}
// init(): root だけからなる path
// add_l(v), add_r(v)：パスの先頭 / 末尾に v を追加
// rm_l(v), rm_r(v)：パスの先頭 / 末尾から v を削除
// query(qid)
template <typename F1, typename F2, typename F3, typename F4, typename F5,
typename F6>
void calc_vertex(F1 init, F2 add_l, F3 add_r, F4 rm_l, F5 rm_r, F6 query) {
const int N = tree.G.N;
auto I = Mo::get_mo_order(LR);
vc<int> FRM(2 * N), TO(2 * N), idx(2 * N);
vc<int> cnt(N);
deque<int> path = {0};
FOR(v, N) {
int a = tree.ELID(v), b = tree.ERID(v);
FRM[a] = tree.parent[v], TO[a] = v;
FRM[b] = v, TO[b] = tree.parent[v];
idx[a] = idx[b] = v;
}
auto flip_left = [&](int i) -> void {
const int a = FRM[i], b = TO[i], c = idx[i];
if (cnt[c] == 0) {
int v = path.front() ^ a ^ b;
path.emplace_front(v), add_l(v);
} else {
int v = path.front();
path.pop_front(), rm_l(v);
}
cnt[c] ^= 1;
};
auto flip_right = [&](int i) -> void {
const int a = FRM[i], b = TO[i], c = idx[i];
if (cnt[c] == 0) {
int v = path.back() ^ a ^ b;
path.emplace_back(v), add_r(v);
} else {
int v = path.back();
path.pop_back(), rm_r(v);
}
cnt[c] ^= 1;
};
init();
int l = 1, r = 1;
for (auto idx: I) {
int L = LR[idx].fi, R = LR[idx].se;
while (l > L) { flip_left(--l); }
while (r < R) { flip_right(r++); }
while (l < L) { flip_left(l++); }
while (r > R) { flip_right(--r); }
query(idx);
}
}
// init(): root だけからなる path
// add_l(frm, to), add_r(frm, to)：パスの先頭 / 末尾に (frm,to) を追加
// rm_l(frm, to), rm_r(frm, to)：パスの先頭 / 末尾に (frm,to) を追加
// query(qid)
template <typename F1, typename F2, typename F3, typename F4, typename F5,
typename F6>
void calc_edge(F1 init, F2 add_l, F3 add_r, F4 rm_l, F5 rm_r, F6 query) {
const int N = tree.G.N;
auto I = Mo::get_mo_order(LR);
vc<int> FRM(2 * N), TO(2 * N), idx(2 * N);
vc<int> cnt(N);
deque<int> path = {0};
FOR(v, N) {
int a = tree.ELID(v), b = tree.ERID(v);
FRM[a] = tree.parent[v], TO[a] = v;
FRM[b] = v, TO[b] = tree.parent[v];
idx[a] = idx[b] = v;
}
auto flip_left = [&](int i) -> void {
const int a = FRM[i], b = TO[i], c = idx[i];
if (cnt[c] == 0) {
int v = path.front() ^ a ^ b;
path.emplace_front(v), add_l(v, v ^ a ^ b);
} else {
int v = path.front();
path.pop_front(), rm_l(v, v ^ a ^ b);
}
cnt[c] ^= 1;
};
auto flip_right = [&](int i) -> void {
const int a = FRM[i], b = TO[i], c = idx[i];
if (cnt[c] == 0) {
int v = path.back() ^ a ^ b;
path.emplace_back(v), add_r(v ^ a ^ b, v);
} else {
int v = path.back();
path.pop_back(), rm_r(v ^ a ^ b, v);
}
cnt[c] ^= 1;
};
init();
int l = 1, r = 1;
for (auto idx: I) {
int L = LR[idx].fi, R = LR[idx].se;
while (l > L) { flip_left(--l); }
while (r < R) { flip_right(r++); }
while (l < L) { flip_left(l++); }
while (r > R) { flip_right(--r); }
query(idx);
}
}
};
#line 2 "graph/ds/tree_monoid.hpp"
#line 2 "ds/segtree/segtree.hpp"
template <class Monoid>
struct SegTree {
using MX = Monoid;
using X = typename MX::value_type;
using value_type = X;
vc<X> dat;
int n, log, size;
SegTree() {}
SegTree(int n) { build(n); }
template <typename F>
SegTree(int n, F f) {
build(n, f);
}
SegTree(const vc<X>& v) { build(v); }
void build(int m) {
build(m, [](int i) -> X { return MX::unit(); });
}
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;
size = 1 << log;
dat.assign(size << 1, MX::unit());
FOR(i, n) dat[size + i] = f(i);
FOR_R(i, 1, size) update(i);
}
X get(int i) { return dat[size + i]; }
vc<X> get_all() { return {dat.begin() + size, dat.begin() + size + n}; }
void update(int i) { dat[i] = Monoid::op(dat[2 * i], dat[2 * i + 1]); }
void set(int i, const X& x) {
assert(i < n);
dat[i += size] = x;
while (i >>= 1) update(i);
}
void multiply(int i, const X& x) {
assert(i < n);
i += size;
dat[i] = Monoid::op(dat[i], x);
while (i >>= 1) update(i);
}
X prod(int L, int R) {
assert(0 <= L && L <= R && R <= n);
X vl = Monoid::unit(), vr = Monoid::unit();
L += size, R += size;
while (L < R) {
if (L & 1) vl = Monoid::op(vl, dat[L++]);
if (R & 1) vr = Monoid::op(dat[--R], vr);
L >>= 1, R >>= 1;
}
return Monoid::op(vl, vr);
}
X prod_all() { return dat[1]; }
template <class F>
int max_right(F check, int L) {
assert(0 <= L && L <= n && check(Monoid::unit()));
if (L == n) return n;
L += size;
X sm = Monoid::unit();
do {
while (L % 2 == 0) L >>= 1;
if (!check(Monoid::op(sm, dat[L]))) {
while (L < size) {
L = 2 * L;
if (check(Monoid::op(sm, dat[L]))) { sm = Monoid::op(sm, dat[L++]); }
}
return L - size;
}
sm = Monoid::op(sm, dat[L++]);
} while ((L & -L) != L);
return n;
}
template <class F>
int min_left(F check, int R) {
assert(0 <= R && R <= n && check(Monoid::unit()));
if (R == 0) return 0;
R += size;
X sm = Monoid::unit();
do {
--R;
while (R > 1 && (R % 2)) R >>= 1;
if (!check(Monoid::op(dat[R], sm))) {
while (R < size) {
R = 2 * R + 1;
if (check(Monoid::op(dat[R], sm))) { sm = Monoid::op(dat[R--], sm); }
}
return R + 1 - size;
}
sm = Monoid::op(dat[R], sm);
} while ((R & -R) != R);
return 0;
}
// prod_{l<=i<r} A[i xor x]
X xor_prod(int l, int r, int xor_val) {
static_assert(Monoid::commute);
X x = Monoid::unit();
for (int k = 0; k < log + 1; ++k) {
if (l >= r) break;
if (l & 1) { x = Monoid::op(x, dat[(size >> k) + ((l++) ^ xor_val)]); }
if (r & 1) { x = Monoid::op(x, dat[(size >> k) + ((--r) ^ xor_val)]); }
l /= 2, r /= 2, xor_val /= 2;
}
return x;
}
};
#line 2 "alg/monoid/monoid_reverse.hpp"
template <class Monoid>
struct Monoid_Reverse {
using value_type = typename Monoid::value_type;
using X = value_type;
static constexpr X op(const X &x, const X &y) { return Monoid::op(y, x); }
static constexpr X unit() { return Monoid::unit(); }
static const bool commute = Monoid::commute;
};
#line 6 "graph/ds/tree_monoid.hpp"
template <typename TREE, typename Monoid, bool edge>
struct Tree_Monoid {
using MX = Monoid;
using X = typename MX::value_type;
TREE &tree;
int N;
SegTree<MX> seg;
SegTree<Monoid_Reverse<MX>> seg_r;
Tree_Monoid(TREE &tree) : tree(tree), N(tree.N) {
build([](int i) -> X { return MX::unit(); });
}
Tree_Monoid(TREE &tree, vc<X> &dat) : tree(tree), N(tree.N) {
build([&](int i) -> X { return dat[i]; });
}
template <typename F>
Tree_Monoid(TREE &tree, F f) : tree(tree), N(tree.N) {
build(f);
}
template <typename F>
void build(F f) {
if (!edge) {
auto f_v = [&](int i) -> X { return f(tree.V[i]); };
seg.build(N, f_v);
if constexpr (!MX::commute) { seg_r.build(N, f_v); }
} else {
auto f_e = [&](int i) -> X { return (i == 0 ? MX::unit() : f(tree.v_to_e(tree.V[i]))); };
seg.build(N, f_e);
if constexpr (!MX::commute) { seg_r.build(N, f_e); }
}
}
void set(int i, X x) {
if constexpr (edge) i = tree.e_to_v(i);
i = tree.LID[i];
seg.set(i, x);
if constexpr (!MX::commute) seg_r.set(i, x);
}
void multiply(int i, X x) {
if constexpr (edge) i = tree.e_to_v(i);
i = tree.LID[i];
seg.multiply(i, x);
if constexpr (!MX::commute) seg_r.multiply(i, x);
}
X prod_path(int u, int v) {
auto pd = tree.get_path_decomposition(u, v, edge);
X val = MX::unit();
for (auto &&[a, b]: pd) { val = MX::op(val, get_prod(a, b)); }
return val;
}
// uv path 上で prod_path(u, x) が check を満たす最後の x
// なければ （つまり path(u,u) が ng ）-1
template <class F>
int max_path(F check, int u, int v) {
if constexpr (edge) return max_path_edge(check, u, v);
if (!check(prod_path(u, u))) return -1;
auto pd = tree.get_path_decomposition(u, v, edge);
X val = MX::unit();
for (auto &&[a, b]: pd) {
X x = get_prod(a, b);
if (check(MX::op(val, x))) {
val = MX::op(val, x);
u = (tree.V[b]);
continue;
}
auto check_tmp = [&](X x) -> bool { return check(MX::op(val, x)); };
if (a <= b) {
// 下り
auto i = seg.max_right(check_tmp, a);
return (i == a ? u : tree.V[i - 1]);
} else {
// 上り
int i = 0;
if constexpr (MX::commute) i = seg.min_left(check_tmp, a + 1);
if constexpr (!MX::commute) i = seg_r.min_left(check_tmp, a + 1);
if (i == a + 1) return u;
return tree.V[i];
}
}
return v;
}
X prod_subtree(int u, int root = -1) {
if (root == u) return prod_all();
if (root == -1 || tree.in_subtree(u, root)) {
int l = tree.LID[u], r = tree.RID[u];
return seg.prod(l + edge, r);
}
assert(!edge); // さぼり
u = tree.jump(u, root, 1);
int L = tree.LID[u], R = tree.RID[u];
return MX::op(seg.prod(0, L), seg.prod(R, N));
}
X prod_all() { return prod_subtree(tree.V[0]); }
inline X get_prod(int a, int b) {
if constexpr (MX::commute) { return (a <= b) ? seg.prod(a, b + 1) : seg.prod(b, a + 1); }
return (a <= b) ? seg.prod(a, b + 1) : seg_r.prod(b, a + 1);
}
private:
template <class F>
int max_path_edge(F check, int u, int v) {
static_assert(edge);
if (!check(MX::unit())) return -1;
int lca = tree.lca(u, v);
auto pd = tree.get_path_decomposition(u, lca, edge);
X val = MX::unit();
// climb
for (auto &&[a, b]: pd) {
assert(a >= b);
X x = get_prod(a, b);
if (check(MX::op(val, x))) {
val = MX::op(val, x);
u = (tree.parent[tree.V[b]]);
continue;
}
auto check_tmp = [&](X x) -> bool { return check(MX::op(val, x)); };
int i = 0;
if constexpr (MX::commute) i = seg.min_left(check_tmp, a + 1);
if constexpr (!MX::commute) i = seg_r.min_left(check_tmp, a + 1);
if (i == a + 1) return u;
return tree.parent[tree.V[i]];
}
// down
pd = tree.get_path_decomposition(lca, v, edge);
for (auto &&[a, b]: pd) {
assert(a <= b);
X x = get_prod(a, b);
if (check(MX::op(val, x))) {
val = MX::op(val, x);
u = (tree.V[b]);
continue;
}
auto check_tmp = [&](X x) -> bool { return check(MX::op(val, x)); };
auto i = seg.max_right(check_tmp, a);
return (i == a ? u : tree.V[i - 1]);
}
return v;
}
};
#line 2 "alg/monoid/affine.hpp"
// op(F, G) = comp(G,F), F のあとで G
template <typename K>
struct Monoid_Affine {
using F = pair<K, K>;
using value_type = F;
using X = value_type;
static constexpr F op(const F &x, const F &y) noexcept {
return F({x.first * y.first, x.second * y.first + y.second});
}
static constexpr F inverse(const F &x) {
auto [a, b] = x;
a = K(1) / a;
return {a, a * (-b)};
}
static constexpr K eval(const F &f, K x) noexcept {
return f.first * x + f.second;
}
static constexpr F unit() { return {K(1), K(0)}; }
static constexpr bool commute = false;
};
#line 2 "alg/monoid/add_pair.hpp"
template <typename E>
struct Monoid_Add_Pair {
using value_type = pair<E, E>;
using X = value_type;
static constexpr X op(const X &x, const X &y) {
return {x.fi + y.fi, x.se + y.se};
}
static constexpr X inverse(const X &x) { return {-x.fi, -x.se}; }
static constexpr X unit() { return {0, 0}; }
static constexpr bool commute = true;
};
#line 2 "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 inv(int n) {
static const int mod = mint::get_mod();
static vector<mint> dat = {0, 1};
assert(0 <= n);
if (n >= mod) n %= mod;
while (len(dat) <= n) {
int k = len(dat);
int q = (mod + k - 1) / k;
dat.eb(dat[k * q - mod] * mint::raw(q));
}
return dat[n];
}
template <typename mint>
mint fact(int n) {
static const int mod = mint::get_mod();
assert(0 <= n && n < mod);
static vector<mint> dat = {1, 1};
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));
return dat[n];
}
template <typename mint>
mint fact_inv(int n) {
static vector<mint> dat = {1, 1};
if (n < 0) return mint(0);
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
return dat[n];
}
template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
return (mint(1) * ... * fact_inv<mint>(xs));
}
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;
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 3 "mod/modint.hpp"
template <int mod>
struct modint {
static constexpr u32 umod = u32(mod);
static_assert(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 {
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};
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 11 "test/1_mytest/mo_on_tree.test.cpp"
using mint = modint998;
using AFF = pair<mint, mint>;
AFF gen() {
mint a = RNG(1, 3);
mint b = RNG(0, 3);
return {a, b};
}
template <typename Mono, bool EDGE>
void test() {
constexpr bool ORIENTED = !(Mono::commute);
FOR(N, 1, 50) {
FOR(Q, 1, 50) {
vc<pi> query(Q);
vc<AFF> dat;
if (!EDGE) {
FOR(v, N) dat.eb(gen());
} else {
FOR(i, N - 1) dat.eb(gen());
}
Graph<int, 0> G(N);
FOR(v, 1, N) {
int p = RNG(0, v);
G.add(p, v);
}
G.build();
Tree<decltype(G)> tree(G);
Tree_Monoid<decltype(tree), Mono, EDGE> TM(tree, dat);
FOR(q, Q) {
int a = RNG(0, N);
int b = RNG(0, N);
query[q] = {a, b};
}
Mo_on_Tree<decltype(tree), ORIENTED> mo(tree);
for (auto&& [a, b]: query) mo.add(a, b);
if constexpr (!EDGE) {
AFF f = Mono::unit();
auto init = [&]() -> void { f = dat[0]; };
auto add_l = [&](int v) -> void { f = Mono::op(dat[v], f); };
auto rm_l = [&](int v) -> void { f = Mono::op(Mono::inverse(dat[v]), f); };
auto add_r = [&](int v) -> void { f = Mono::op(f, dat[v]); };
auto rm_r = [&](int v) -> void { f = Mono::op(f, Mono::inverse(dat[v])); };
auto ans = [&](int q) -> void { assert(f == TM.prod_path(query[q].fi, query[q].se)); };
mo.calc_vertex(init, add_l, add_r, rm_l, rm_r, ans);
} else {
AFF f = Mono::unit();
auto get = [&](int a, int b) -> int { return tree.v_to_e((tree.parent[a] == b ? a : b)); };
auto init = [&]() -> void {};
auto add_l = [&](int a, int b) -> void { f = Mono::op(dat[get(a, b)], f); };
auto rm_l = [&](int a, int b) -> void { f = Mono::op(Mono::inverse(dat[get(a, b)]), f); };
auto add_r = [&](int a, int b) -> void { f = Mono::op(f, dat[get(a, b)]); };
auto rm_r = [&](int a, int b) -> void { f = Mono::op(f, Mono::inverse(dat[get(a, b)])); };
auto ans = [&](int q) -> void { assert(f == TM.prod_path(query[q].fi, query[q].se)); };
mo.calc_edge(init, add_l, add_r, rm_l, rm_r, ans);
}
}
}
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
// パスの向きが可逆で頂点可換モノイド積
test<Monoid_Add_Pair<mint>, false>();
// パスの向きが不可逆で頂点非可換モノイド積
test<Monoid_Affine<mint>, false>();
// パスの向きが可逆で辺可換モノイド積
test<Monoid_Add_Pair<mint>, true>();
// パスの向きが不可逆で辺非可換モノイド積
test<Monoid_Affine<mint>, true>();
solve();
return 0;
}