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test/library_checker/datastructure/dynamic_tree_vertex_set_path_composite.test.cpp
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- Last update: 2024-04-27 11:55:26+09:00
- Problem: https://judge.yosupo.jp/problem/dynamic_tree_vertex_set_path_composite
Depends on
- alg/monoid/affine.hpp
- graph/ds/lct_node_monoid.hpp
- graph/ds/link_cut_tree.hpp
- mod/modint.hpp
- mod/modint_common.hpp
- my_template.hpp
- other/io.hpp
Code
#define PROBLEM \
"https://judge.yosupo.jp/problem/dynamic_tree_vertex_set_path_composite"
#include "my_template.hpp"
#include "other/io.hpp"
#include "graph/ds/link_cut_tree.hpp"
#include "graph/ds/lct_node_monoid.hpp"
#include "alg/monoid/affine.hpp"
#include "mod/modint.hpp"
using mint = modint998;
using Mono = Monoid_Affine<mint>;
using Node = LCT_Node_Monoid<Mono>;
void solve() {
LL(N, Q);
Link_Cut_Tree<Node> LCT(N);
FOR(i, N) {
mint a, b;
read(a, b);
LCT.set(i, {a, b});
}
FOR(N - 1) {
INT(a, b);
LCT.link(a, b);
}
FOR(Q) {
LL(t);
if (t == 0) {
LL(a, b, c, d);
LCT.cut(a, b), LCT.link(c, d);
}
if (t == 1) {
LL(i);
mint a, b;
read(a, b);
LCT.set(i, {a, b});
}
if (t == 2) {
LL(a, b);
auto f = LCT.prod_path(a, b);
u32 x;
read(x);
mint ans = Mono::eval(f, mint::raw(x));
print(ans);
}
}
}
signed main() {
solve();
return 0;
}#line 1 "test/library_checker/datastructure/dynamic_tree_vertex_set_path_composite.test.cpp"
#define PROBLEM \
"https://judge.yosupo.jp/problem/dynamic_tree_vertex_set_path_composite"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
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 FOR_subset(t, s) \
for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#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_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (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 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;
}
#endif
#line 1 "other/io.hpp"
#define FASTIO
#include <unistd.h>
// 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;
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() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T>
void rd_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
x = 0;
while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus) x = -x;
}
}
void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }
template <class T, class U>
void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T>
void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T>
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);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ) flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c: s) wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) wt(s[i]);
}
template <typename T>
void wt_integer(T x) {
if (por > SZ - 100) flush();
if (x < 0) { obuf[por++] = '-', x = -x; }
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }
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 < std::tuple_size<T>::value) {
if constexpr (N > 0) { wt(' '); }
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T>
void wt(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(head);
if (sizeof...(Tail)) wt(' ');
print(forward<Tail>(tail)...);
}
// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;
#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); }
#line 5 "test/library_checker/datastructure/dynamic_tree_vertex_set_path_composite.test.cpp"
#line 1 "graph/ds/link_cut_tree.hpp"
/*
各 heavy path を head が左, tail が右となるように splay tree で持つ.
ユーザーが直接呼ぶ可能性があるものだけ int でも実装.
LCT 外で探索するときなど，push を忘れないように注意.
*/
template <typename Node>
struct Link_Cut_Tree {
using np = Node *;
int n;
vc<Node> nodes;
Link_Cut_Tree(int n = 0) : n(n), nodes(n) { FOR(i, n) nodes[i] = Node(i); }
Node *operator[](int v) { return &nodes[v]; }
// underlying tree の根
Node *get_root(Node *c) {
expose(c);
c->push();
while (c->l) {
c = c->l;
c->push();
}
splay(c);
return c;
}
// underlying tree の根
int get_root(int c) { return get_root(&nodes[c])->idx; }
// parent(c)==p となるように link.
void link(Node *c, Node *p) {
evert(c);
expose(p);
p->push();
// no edge -> heavy edge
assert(!(c->p));
assert(!(p->r));
c->p = p;
p->r = c;
p->update();
}
// parent(c)==p となるように link.
void link(int c, int p) { return link(&nodes[c], &nodes[p]); }
void cut(Node *a, Node *b) {
evert(a);
expose(b);
assert(!b->p);
assert((b->l) == a);
// heavy edge -> no edge
b->l->p = nullptr;
b->l = nullptr;
b->update();
}
void cut(int a, int b) { return cut(&nodes[a], &nodes[b]); }
// c を underlying tree の根とする.
// c は splay tree の根にもなる.
// c は push 済になる
void evert(Node *c) {
expose(c);
c->reverse();
c->push();
}
// c を underlying tree の根とする.
// c は splay tree の根にもなる.
void evert(int c) { evert(&nodes[c]); }
Node *lca(Node *u, Node *v) {
assert(get_root(u) == get_root(v));
expose(u);
return expose(v);
}
int lca(int u, int v) { return lca(&nodes[u], &nodes[v])->idx; }
// 辺の個数
int dist(int u, int v) {
evert(u), expose(v);
return ((*this)[v]->size) - 1;
}
Node *jump(Node *u, Node *v, int k) {
evert(v);
expose(u);
assert(0 <= k && k < (u->size));
while (1) {
u->push();
int rs = (u->r ? u->r->size : 0);
if (k < rs) {
u = u->r;
continue;
}
if (k == rs) { break; }
k -= rs + 1;
u = u->l;
}
splay(u);
return u;
}
int jump(int u, int v, int k) {
auto c = jump((*this)[u], (*this)[v], k);
return c->idx;
}
// [root, c] がひとつの splay tree になるように変更する.
// c が右端で splay tree の根という状態になる.
// path query はこの状態で c の data を見る.
// c は push 済になる
virtual Node *expose(Node *c) {
Node *now = c;
Node *rp = nullptr; // 今まで作ったパス
while (now) {
splay(now);
// heavy -> light, light -> heavy.
if (now->r) { now->add_light(now->r); }
if (rp) { now->erase_light(rp); }
now->r = rp;
now->update();
rp = now;
now = now->p;
}
splay(c);
return rp;
}
// [root, c] がひとつの splay tree になるように変更する.
// c が右端で splay tree の根という状態になる.
// path query はこの状態で c の data を見る.
int expose(int c) {
Node *x = expose(&nodes[c]);
if (!x) return -1;
return x->idx;
}
Node *get_parent(Node *x) {
expose(x);
if (!x->l) return nullptr;
x = x->l;
while (x->r) x = x->r;
return x;
}
int get_parent(int x) {
Node *p = get_parent((*this)[x]);
return (p ? p->idx : -1);
}
void set(Node *c, typename Node::VX x) {
evert(c);
c->set(x);
}
void set(int c, typename Node::VX x) { set((*this)[c], x); }
typename Node::X prod_path(int a, int b) {
evert(a), expose(b);
return (*this)[b]->x;
}
// subtree 用の node を使う
typename Node::X prod_subtree(int v, int root) {
static_assert(Node::NODE_FOR_SUBTREE);
if (v == root) {
evert(root);
return (*this)[root]->x;
}
root = jump(v, root, 1);
cut(v, root);
typename Node::X res = (*this)[v]->x;
link(v, root);
return res;
}
vc<int> collect_heavy_path(int v) {
np c = (*this)[v];
while (!is_root(c)) c = c->p;
vc<int> res;
auto dfs = [&](auto &dfs, np c, bool rev) -> void {
if (!rev) {
if (c->l) dfs(dfs, c->l, rev ^ c->rev);
res.eb(c->idx);
if (c->r) dfs(dfs, c->r, rev ^ c->rev);
} else {
if (c->r) dfs(dfs, c->r, rev ^ c->rev);
res.eb(c->idx);
if (c->l) dfs(dfs, c->l, rev ^ c->rev);
}
};
dfs(dfs, c, false);
return res;
}
void debug() {
print("p, l, r, rev");
auto f = [&](np c) -> int { return (c ? c->idx : -1); };
FOR(i, len(nodes)) {
print(i, ",", f((*this)[i]->p), f((*this)[i]->l), f((*this)[i]->r),
(*this)[i]->rev);
}
FOR(i, len(nodes)) {
np c = (*this)[i];
if (c->l) assert(c->l->p == c);
if (c->r) assert(c->r->p == c);
}
}
private:
// splay tree 内で完結する操作. 特に heavy, light 構造は変わらない.
// light pointer は rotate 内でケア
// c は push 済になる
void splay(Node *c) {
c->push();
while (!is_root(c)) {
Node *p = c->p;
Node *pp = (p ? p->p : nullptr);
if (state(p) == 0) {
p->push(), c->push();
rotate(c);
}
elif (state(c) == state(p)) {
pp->push(), p->push(), c->push();
rotate(p);
rotate(c);
}
else {
pp->push(), p->push(), c->push();
rotate(c);
rotate(c);
}
}
}
// パスを表す splay tree の根になっているかどうか
// underlying tree ではない
bool is_root(Node *c) { return state(c) == 0; }
// splay tree 内で完結する操作. 特に heavy, light 構造は変わらない.
// light edge のポインタは変更されうる
void rotate(Node *n) {
// n を根に近づける
Node *pp, *p, *c;
p = n->p;
pp = p->p;
if (p->l == n) {
c = n->r;
n->r = p;
p->l = c;
} else {
c = n->l;
n->l = p;
p->r = c;
}
p->update(), n->update();
if (pp) {
if (pp->l == p) pp->l = n;
elif (pp->r == p) pp->r = n;
else {
// light edge pointer が (pp-p) から (pp-n) に変わる
pp->change_light(p, n);
}
}
n->p = pp;
p->p = n;
if (c) c->p = p;
}
inline int state(Node *n) {
if (!n->p) return 0;
if (n->p->l == n) return 1;
if (n->p->r == n) return -1;
return 0;
}
};
#line 1 "graph/ds/lct_node_monoid.hpp"
template <typename Monoid>
struct LCT_Node_Monoid {
using np = LCT_Node_Monoid *;
// デフォルト
np l, r, p;
int idx, size; // size は heavy path の頂点数
bool rev;
// 目的ごとに定義する.
using MX = Monoid;
using X = typename MX::value_type;
using VX = X;
X x, rx, vx;
LCT_Node_Monoid(int i = 0)
: l(nullptr),
r(nullptr),
p(nullptr),
idx(i),
size(1),
rev(0),
x(MX::unit()),
rx(MX::unit()),
vx(MX::unit()) {}
void update() {
size = 1;
x = vx, rx = vx;
if (l) {
size += l->size, x = Monoid::op(l->x, x), rx = Monoid::op(rx, l->rx);
}
if (r) {
size += r->size, x = Monoid::op(x, r->x), rx = Monoid::op(r->rx, rx);
}
}
void push() {
if (rev) {
if (l) l->reverse();
if (r) r->reverse();
rev = 0;
}
}
// data の reverse も行う
void reverse() {
rev ^= 1;
swap(l, r);
swap(x, rx);
}
// LCT 内で expose, update を行うのでここは変更だけ
void set(VX x) { vx = x; }
void add_light(np c) {}
void erase_light(np c) {}
void change_light(np a, np b) {}
};
#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 "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) {
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 == 1045430273) return {20, 363};
if (mod == 1051721729) return {20, 330};
if (mod == 1053818881) return {20, 2789};
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 10 "test/library_checker/datastructure/dynamic_tree_vertex_set_path_composite.test.cpp"
using mint = modint998;
using Mono = Monoid_Affine<mint>;
using Node = LCT_Node_Monoid<Mono>;
void solve() {
LL(N, Q);
Link_Cut_Tree<Node> LCT(N);
FOR(i, N) {
mint a, b;
read(a, b);
LCT.set(i, {a, b});
}
FOR(N - 1) {
INT(a, b);
LCT.link(a, b);
}
FOR(Q) {
LL(t);
if (t == 0) {
LL(a, b, c, d);
LCT.cut(a, b), LCT.link(c, d);
}
if (t == 1) {
LL(i);
mint a, b;
read(a, b);
LCT.set(i, {a, b});
}
if (t == 2) {
LL(a, b);
auto f = LCT.prod_path(a, b);
u32 x;
read(x);
mint ans = Mono::eval(f, mint::raw(x));
print(ans);
}
}
}
signed main() {
solve();
return 0;
}