test/yosupo/vertex_set_path_composite.test.cpp

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Last update: 2023-06-25 16:24:15+09:00
Problem: https://judge.yosupo.jp/problem/vertex_set_path_composite

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite"
#include "../../math/StaticModInt.hpp"
#include "../../data-structure/SegTree.hpp"
#include "../../graph/HeavyLightDecomposition.hpp"
#include "../../basic/template.hpp"
using ModInt = StaticModInt<998244353>;
using MP = std::pair<ModInt, ModInt>;
MP nodef(const MP& lhs, const MP& rhs) {
	return {lhs.first * rhs.first, lhs.second * rhs.first + rhs.second};
}
class MySeg : public SegTree<MP, nodef> {
	using Base = SegTree<MP, nodef>;

  public:
	MySeg(int n) : Base(n, MP{1, 0}, MP{1, 0}) {}
};
int n, q;
IP a[200010];
int main() {
	scanf("%d%d", &n, &q);
	rep(i, n) scanf("%d%d", &a[i].first, &a[i].second);
	HeavyLightDecomposition hld(n);
	MySeg st1(n), st2(n);
	rep(i, n - 1) {
		int u, v;
		scanf("%d%d", &u, &v);
		hld.add_edge(u, v);
	}
	hld.build(0);
	rep(i, n) {
		st1.update(hld.label[i], a[i]);
		st2.update(n - 1 - hld.label[i], a[i]);
	}
	rep(i, q) {
		int t;
		scanf("%d", &t);
		if (t == 0) {
			int p, c, d;
			scanf("%d%d%d", &p, &c, &d);
			a[p] = {c, d};
			st1.update(hld.label[p], {c, d});
			st2.update(n - 1 - hld.label[p], {c, d});
		} else {
			int u, v, x;
			scanf("%d%d%d", &u, &v, &x);
			int t = hld.lca(u, v);
			std::pair<ModInt, ModInt> f1(1, 0), f2(1, 0);
			hld.each_vertex(u, t, [&](int l, int r) {
				auto p = st2.query(n - 1 - r, n - 1 - l + 1);
				f1 = {f1.first * p.first, f1.second * p.first + p.second};
			});
			f1 = {f1.first / a[t].first,
				  (f1.second - a[t].second) / a[t].first};
			hld.each_vertex(t, v, [&](int l, int r) {
				auto p = st1.query(l, r + 1);
				f2 = {p.first * f2.first, p.second * f2.first + f2.second};
			});
			f1 = {f1.first * f2.first, f1.second * f2.first + f2.second};
			printf("%d\n", ModInt(x) * f1.first + f1.second);
		}
	}
}

#line 1 "test/yosupo/vertex_set_path_composite.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite"
#line 2 "basic/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#ifndef __clang__
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
#include <string.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define rep(i, n) for (int i = 0; i < int(n); i++)
#define REP(i, n) for (int i = 1; i <= int(n); i++)
#define all(V) V.begin(), V.end()

using i128 = __int128_t;
using u128 = __uint128_t;
using uint = unsigned int;
using lint = long long;
using ulint = unsigned long long;
using IP = std::pair<int, int>;
using LP = std::pair<lint, lint>;

constexpr int INF = INT_MAX / 2;
constexpr lint LINF = LLONG_MAX / 2;
constexpr double eps = DBL_EPSILON * 10;
constexpr double PI = 3.141592653589793238462643383279;

template <class T>
class prique : public std::priority_queue<T, std::vector<T>, std::greater<T>> {};
int popcount(uint x) {
#if __cplusplus >= 202002L
	return std::popcount(x);
#else
#ifndef __clang__
	return __builtin_popcount(x);
#endif
#endif
	x = (x & 0x55555555) + (x >> 1 & 0x55555555);
	x = (x & 0x33333333) + (x >> 2 & 0x33333333);
	x = (x & 0x0f0f0f0f) + (x >> 4 & 0x0f0f0f0f);
	x = (x & 0x00ff00ff) + (x >> 8 & 0x00ff00ff);
	return (x & 0x0000ffff) + (x >> 16 & 0x0000ffff);
}
template <class F>
inline constexpr decltype(auto) lambda_fix(F&& f) {
	return [f = std::forward<F>(f)](auto&&... args) {
		return f(f, std::forward<decltype(args)>(args)...);
	};
}
template <class T>
constexpr std::vector<T> make_vec(size_t n) {
	return std::vector<T>(n);
}
template <class T, class... Args>
constexpr auto make_vec(size_t n, Args&&... args) {
	return std::vector<decltype(make_vec<T>(args...))>(n, make_vec<T>(std::forward<Args>(args)...));
}
template <class T, class U, class Stream>
Stream& operator>>(Stream& ist, std::pair<T, U>& x) {
	return ist >> x.first >> x.second;
}
template <class T, class U, class Stream>
Stream& operator<<(Stream& ost, const std::pair<T, U>& x) {
	return ost << x.first << " " << x.second;
}
template <class Container,
		  std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator>>(std::istream& ist, Container& cont)
	-> decltype(typename Container::iterator(), std::cin)& {
	Container tmp;
	while (true) {
		typename Container::value_type t;
		ist >> t;
		tmp.emplace_back(t);
		if (getchar() == '\n') break;
	}
	cont = Container(std::move(tmp));
	return ist;
}
template <class Container, class Stream,
		  std::enable_if_t<!std::is_same<Container, std::string>::value, std::nullptr_t> = nullptr>
auto operator<<(Stream& ost, const Container& cont)
	-> decltype(typename Container::iterator(), ost)& {
	for (auto it = cont.begin(); it != cont.end(); it++) {
		if (it != cont.begin()) ost << ' ';
		ost << *it;
	}
	return ost;
}
template <class Container>
auto sum(const Container& cont) -> decltype(typename Container::iterator(), 0LL) {
	lint res = 0;
	for (auto it = cont.begin(); it != cont.end(); it++) res += *it;
	return res;
}
template <class T, class U>
constexpr inline bool chmax(T& lhs, const U& rhs) noexcept {
	if (lhs < rhs) {
		lhs = rhs;
		return true;
	}
	return false;
}
template <class T, class U>
constexpr inline bool chmin(T& lhs, const U& rhs) noexcept {
	if (lhs > rhs) {
		lhs = rhs;
		return true;
	}
	return false;
}
constexpr inline lint gcd(lint a, lint b) noexcept {
	while (b) {
		lint c = a;
		a = b;
		b = c % b;
	}
	return a;
}
inline lint lcm(lint a, lint b) noexcept { return a / gcd(a, b) * b; }
constexpr bool isprime(lint n) noexcept {
	if (n == 1) return false;
	for (int i = 2; i * i <= n; i++) {
		if (n % i == 0) return false;
	}
	return true;
}
template <class T>
constexpr T mypow(T a, lint b) noexcept {
	T res(1);
	while (true) {
		if (b & 1) res *= a;
		b >>= 1;
		if (!b) break;
		a *= a;
	}
	return res;
}
constexpr lint modpow(lint a, lint b, lint m) noexcept {
	a %= m;
	lint res(1);
	while (b) {
		if (b & 1) res *= a, res %= m;
		a *= a, a %= m, b >>= 1;
	}
	return res;
}
LP extGcd(lint a, lint b) noexcept {
	if (b == 0) return {1, 0};
	LP s = extGcd(b, a % b);
	std::swap(s.first, s.second);
	s.second -= a / b * s.first;
	return s;
}
LP ChineseRem(const lint& b1, const lint& m1, const lint& b2, const lint& m2) noexcept {
	auto p = extGcd(m1, m2);
	lint g = gcd(m1, m2), l = m1 / g * m2;
	lint tmp = (b2 - b1) / g * p.first % (m2 / g);
	lint r = (b1 + m1 * tmp + l) % l;
	return {r, l};
}
int LCS(const std::string& a, const std::string& b) {
	auto dp = make_vec<int>(a.size() + 1, b.size() + 1);
	rep(i, a.size()) {
		rep(j, b.size()) {
			chmax(dp[i + 1][j], dp[i][j]);
			chmax(dp[i][j + 1], dp[i][j]);
			if (a[i] == b[j]) chmax(dp[i + 1][j + 1], dp[i][j] + 1);
		}
		chmax(dp[i + 1][b.size()], dp[i][b.size()]);
	}
	rep(j, b.size()) chmax(dp[a.size()][j + 1], dp[a.size()][j]);
	return dp[a.size()][b.size()];
}
template <class T, std::enable_if_t<std::is_convertible<int, T>::value, std::nullptr_t> = nullptr>
void compress(std::vector<T>& vec) {
	auto tmp = vec;
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (T& i : vec) i = std::lower_bound(all(tmp), i) - tmp.begin();
}
template <class T>
void compress(T* l, T* r) {
	std::vector<T> tmp(l, r);
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (auto i = l; i < r; i++) {
		*i = std::lower_bound(all(tmp), *i) - tmp.begin();
	}
}
template <class InputIter>
void compress(InputIter l, InputIter r) {
	std::vector<typename InputIter::value_type> tmp(l, r);
	std::sort(all(tmp));
	tmp.erase(std::unique(all(tmp)), tmp.end());
	for (auto i = l; i < r; i++) {
		*i = std::lower_bound(all(tmp), *i) - tmp.begin();
	}
}
template <class InputIter,
		  std::enable_if_t<std::is_same<typename InputIter::value_type, std::pair<IP, int>>::value,
						   std::nullptr_t> = nullptr>
void mo_sort(InputIter l, InputIter r, int N) {
	const int M = std::max(1.0, std::sqrt(lint(N) * N / std::distance(l, r)));
	std::sort(l, r, [M](const auto& lhs, const auto& rhs) {
		if (lhs.first.first / M < rhs.first.first / M) return true;
		if (lhs.first.first / M == rhs.first.first / M) return lhs.first.second < rhs.first.second;
		return false;
	});
	int before = -1, cnt = 0;
	bool f = false;
	for (InputIter i = l; i != r; i++) {
		if (before != i->first.first / M) {
			if (f) std::reverse(i - cnt, i);
			f ^= true, before = i->first.first / M, cnt = 1;
		} else
			cnt++;
	}
	if (f) std::reverse(r - cnt, r);
}
template <class T>
std::vector<T> xor_bases(const std::vector<T>& vec) {
	std::vector<T> res;
	for (T i : vec) {
		for (T j : res) {
			chmin(i, i ^ j);
		}
		if (i) res.emplace_back(i);
	}
	return res;
}
#line 3 "basic/type_traits.hpp"

class ModInt__Base {};
class StaticModInt__Base : ModInt__Base {};
class DynamicModInt__Base : ModInt__Base {};

template <class T>
class is_ModInt : public std::is_base_of<ModInt__Base, T> {};
template <class T>
constexpr bool is_ModInt_v = is_ModInt<T>::value;

template <class T>
class is_StaticModInt : public std::is_base_of<StaticModInt__Base, T> {};
template <class T>
constexpr bool is_StaticModInt_v = is_StaticModInt<T>::value;

template <class T>
class is_DynamicModInt : public std::is_base_of<DynamicModInt__Base, T> {};
template <class T>
constexpr bool is_DynamicModInt_v = is_DynamicModInt<T>::value;
#line 4 "math/StaticModInt.hpp"
template <int modulo>
class StaticModInt : StaticModInt__Base {
	uint value;
	static constexpr int inv1000000007[] = {0,		   1,		  500000004, 333333336,
											250000002, 400000003, 166666668, 142857144,
											125000001, 111111112, 700000005},
						 inv998244353[] = {0,		  1,		 499122177, 332748118,
										   748683265, 598946612, 166374059, 855638017,
										   873463809, 443664157, 299473306};

  public:
	static constexpr int mod_value = modulo;

	constexpr StaticModInt() : value(0) {}
	template <class T, std::enable_if_t<!std::is_convertible<T, StaticModInt>::value,
										std::nullptr_t> = nullptr>
	constexpr StaticModInt(T value = 0) : value(value % modulo) {
		if (this->value < 0) this->value += modulo;
	}
	inline constexpr StaticModInt inv() const {
		if constexpr (modulo == 1000000007) {
			if (*this <= 10) return inv1000000007[*this];
		} else if constexpr (modulo == 998244353) {
			if (*this <= 10) return inv998244353[*this];
		}
		return mypow(*this, modulo - 2);
	}
	inline constexpr StaticModInt pow(lint k) const { return mypow(*this, k); }
	inline constexpr operator int() const { return value; }
	inline constexpr StaticModInt& operator+=(const StaticModInt& x) {
		value = value + x.value;
		if (value >= modulo) value -= modulo;
		return *this;
	}
	inline constexpr StaticModInt& operator++() {
		if (value == modulo - 1)
			value = 0;
		else
			value++;
		return *this;
	}
	inline constexpr StaticModInt operator++(int) {
		StaticModInt res = *this;
		++*this;
		return res;
	}
	inline constexpr StaticModInt operator-() const { return StaticModInt(0) -= *this; }
	inline constexpr StaticModInt& operator-=(const StaticModInt& x) {
		if (value < x.value) value += modulo;
		value -= x.value;
		return *this;
	}
	inline constexpr StaticModInt& operator--() {
		if (value == 0)
			value = modulo - 1;
		else
			value--;
		return *this;
	}
	inline constexpr StaticModInt operator--(int) {
		StaticModInt res = *this;
		--*this;
		return res;
	}
	inline constexpr StaticModInt& operator*=(const StaticModInt& x) {
		value = (ulint)value * x.value % modulo;
		return *this;
	}
	inline constexpr StaticModInt& operator/=(const StaticModInt& rhs) {
		return *this *= rhs.inv();
	}
	template <class T>
	constexpr StaticModInt operator+(const T& rhs) const {
		return StaticModInt(*this) += rhs;
	}
	template <class T>
	constexpr StaticModInt& operator+=(const T& rhs) {
		return operator+=(StaticModInt(rhs));
	}
	template <class T>
	constexpr StaticModInt operator-(const T& rhs) const {
		return StaticModInt(*this) -= rhs;
	}
	template <class T>
	constexpr StaticModInt& operator-=(const T& rhs) {
		return operator-=(StaticModInt(rhs));
	}
	template <class T>
	constexpr StaticModInt operator*(const T& rhs) const {
		return StaticModInt(*this) *= rhs;
	}
	template <class T>
	constexpr StaticModInt& operator*=(const T& rhs) {
		return operator*=(StaticModInt(rhs));
	}
	template <class T>
	constexpr StaticModInt operator/(const T& rhs) const {
		return StaticModInt(*this) /= rhs;
	}
	template <class T>
	constexpr StaticModInt& operator/=(const T& rhs) {
		return operator/=(StaticModInt(rhs));
	}
	static StaticModInt primitive_root() {
		if constexpr (modulo == 1012924417) return 5;
		if constexpr (modulo == 924844033) return 5;
		if constexpr (modulo == 998244353) return 3;
		if constexpr (modulo == 1224736769) return 3;
		if constexpr (modulo == 167772161) return 3;
		if constexpr (modulo == 469762049) return 3;
		if constexpr (modulo == 1107296257) return 10;

		int p = 0;
		std::mt19937 mt(0);
		std::uniform_int_distribution<> uid(1, modulo - 1);
		if (p) return p;

		// use naive factorize due to file size limit
		std::vector<int> vec;
		int tmp = modulo - 1;
		for (int i = 2; i * i <= tmp; i++) {
			if (tmp % i == 0) {
				vec.emplace_back(i);
				do {
					tmp /= i;
				} while (tmp % i == 0);
			}
		}
		if (tmp != 1) vec.emplace_back(tmp);

		while (true) {
			p = uid(mt);
			bool f = true;
			for (const auto& i : vec) {
				if (mypow(StaticModInt(p), (modulo - 1) / i) == 1) {
					f = false;
					break;
				}
			}
			if (f) return p;
		}
	}
};
template <int modulo, class Stream>
Stream& operator>>(Stream& ist, StaticModInt<modulo>& x) {
	lint a;
	ist >> a;
	x = a;
	return ist;
}
template <int modulo, class Stream>
Stream& operator<<(Stream& ost, const StaticModInt<modulo>& x) {
	ost << int(x);
	return ost;
}

#if __cplusplus < 201703L
template <int modulo>
constexpr int StaticModInt<modulo>::inv1000000007[];
template <int modulo>
constexpr int StaticModInt<modulo>::inv998244353[];
#endif

/**
 * @title StaticModInt
 */
#line 3 "data-structure/SegTree.hpp"
template <class T, T (*nodef)(const T&, const T&)>
class SegTree {
  protected:
	unsigned int n = 1, m = 1, rank = 0;
	std::vector<T> node;
	T ident;

  public:
	SegTree(T e_) : ident(e_) {}
	SegTree(unsigned int m_, T e_) : m(m_), ident(e_) {
		while (n < m) {
			n *= 2;
			rank++;
		}
		node.resize(2 * n, ident);
	}
	SegTree(unsigned int m_, T init, T e_) : m(m_), ident(e_) {
		while (n < m) {
			n *= 2;
			rank++;
		}
		node.resize(2 * n, ident);
		for (unsigned int i = n; i < 2 * n; i++) node[i] = init;
		for (unsigned int i = n - 1; i > 0; i--) node[i] = nodef(node[i << 1], node[i << 1 | 1]);
	}
	template <class U>
	SegTree(const std::vector<U>& initvec, T e_) : ident(e_) {
		m = initvec.size();
		while (n < m) {
			n *= 2;
			rank++;
		}
		node.resize(2 * n, ident);
		for (unsigned int i = n; i < 2 * n; i++) {
			if (i - n < m) node[i] = initvec[i - n];
		}
		for (unsigned int i = n - 1; i > 0; i--) node[i] = nodef(node[i << 1], node[i << 1 | 1]);
	}
	void update(int i, T x) {
		i += n;
		node[i] = x;
		while (i != 1) {
			i >>= 1;
			node[i] = nodef(node[2 * i], node[2 * i + 1]);
		}
	}
	T query(int l, int r) const {
		l += n;
		r += n;
		T ls = ident, rs = ident;
		while (l < r) {
			if (l & 1) ls = nodef(ls, node[l++]);
			if (r & 1) rs = nodef(node[--r], rs);
			l >>= 1;
			r >>= 1;
		}
		return nodef(ls, rs);
	}
	const T& operator[](const int& i) const { return node[n + i]; }
	T query_all() const { return node[1]; }
	void fill(T x) {
		for (unsigned int i = n; i < 2 * n; i++) node[i] = x;
		for (unsigned int i = n - 1; i > 0; i--) node[i] = nodef(node[i << 1], node[i << 1 | 1]);
	}

  private:
	template <class F>
	int max_right(int st, F& check, T& acc, int k, int l, int r) const {
		if (l + 1 == r) {
			acc = nodef(acc, node[k]);
			return check(acc) ? m : k - n;
		}
		int mid = (l + r) >> 1;
		if (mid <= st) return max_right(st, check, acc, (k << 1) | 1, mid, r);
		if (st <= l && check(nodef(acc, node[k]))) {
			acc = nodef(acc, node[k]);
			return m;
		}
		int vl = max_right(st, check, acc, k << 1, l, mid);
		if (vl != m) return vl;
		return max_right(st, check, acc, (k << 1) | 1, mid, r);
	}

	template <class F>
	int min_left(int st, F& check, T& acc, int k, int l, int r) const {
		if (l + 1 == r) {
			acc = nodef(node[k], acc);
			return check(acc) ? 0 : k - n + 1;
		}
		int mid = (l + r) >> 1;
		if (st <= mid) return min_left(st, check, acc, k << 1, l, mid);
		if (r <= st && check(nodef(node[k], acc))) {
			acc = nodef(node[k], acc);
			return 0;
		}
		int vr = min_left(st, check, acc, (k << 1) | 1, mid, r);
		if (vr != 0) return vr;
		return min_left(st, check, acc, k << 1, l, mid);
	}

  public:
	template <class F>
	int max_right(int st, F check) const {
		T acc = ident;
		return max_right(st, check, acc, 1, 0, n);
	}
	template <bool (*check)(const T&)>
	int max_right(int st) const {
		T acc = ident;
		return max_right(st, check, acc, 1, 0, n);
	}

	template <class F>
	int min_left(int st, F check) const {
		T acc = ident;
		return min_left(st, check, acc, 1, 0, n);
	}
	template <bool (*check)(const T&)>
	int min_left(int st) const {
		T acc = ident;
		return min_left(st, check, acc, 1, 0, n);
	}
};
namespace {
	template <typename T>
	T RSQ_nodef(const T& lhs, const T& rhs) {
		return lhs + rhs;
	}
	template <typename T>
	T RMiQ_nodef(const T& lhs, const T& rhs) {
		return std::min(lhs, rhs);
	}
	template <typename T>
	T RMaQ_nodef(const T& lhs, const T& rhs) {
		return std::max(lhs, rhs);
	}
}  // namespace

template <typename T>
class RSQ : public SegTree<T, RSQ_nodef> {
	using Base = SegTree<T, RSQ_nodef>;

  public:
	template <class... Args>
	RSQ(Args&&... args) : Base(std::forward<Args>(args)..., 0) {}
};

template <typename T, typename U = void>
class RMiQ : public SegTree<T, RMiQ_nodef> {
	using Base = SegTree<T, RMiQ_nodef>;

  public:
	template <class... Args>
	RMiQ(Args&&... args) : Base(std::forward<Args>(args)...) {}
};
template <typename T>
class RMiQ<T, std::enable_if_t<std::numeric_limits<T>::is_specialized>>
	: public SegTree<T, RMiQ_nodef> {
	using Base = SegTree<T, RMiQ_nodef>;

  public:
	template <class... Args>
	RMiQ(Args&&... args) : Base(std::forward<Args>(args)..., std::numeric_limits<T>::max()) {}
};

template <typename T, typename U = void>
class RMaQ : public SegTree<T, RMaQ_nodef> {
	using Base = SegTree<T, RMaQ_nodef>;

  public:
	template <class... Args>
	RMaQ(Args&&... args) : Base(std::forward<Args>(args)...) {}
};
template <typename T>
class RMaQ<T, std::enable_if_t<std::numeric_limits<T>::is_specialized>>
	: public SegTree<T, RMaQ_nodef> {
	using Base = SegTree<T, RMaQ_nodef>;

  public:
	template <class... Args>
	RMaQ(Args&&... args) : Base(std::forward<Args>(args)..., std::numeric_limits<T>::min()) {}
};
#line 3 "graph/HeavyLightDecomposition.hpp"
class HeavyLightDecomposition {
	int n, index = 0;
	void size_dfs(int node) {
		size[node] = 1;
		for (int& i : vec[node]) {
			if (par[node] == i) continue;
			par[i] = node;
			size_dfs(i);
			size[node] += size[i];
			if (size[i] > size[vec[node][0]]) std::swap(i, vec[node][0]);
		}
	}
	void build_dfs(int node) {
		label[node] = index++;
		for (int& i : vec[node]) {
			if (par[node] != i) {
				head[i] = (i == vec[node][0] ? head[node] : i);
				build_dfs(i);
			}
		}
		last[node] = index;
	}

  public:
	std::vector<std::vector<int>> vec;
	std::vector<int> size, par, head, label, last;
	HeavyLightDecomposition() {}
	HeavyLightDecomposition(int m) : n(m) { init(n); }
	void init(int m) {
		n = m;
		vec.resize(n), size.resize(n), par.resize(n), head.resize(n), label.resize(n),
			last.resize(n);
	}
	void add_edge(int u, int v) { vec[u].emplace_back(v), vec[v].emplace_back(u); }
	void build(int root) {
		std::fill(all(par), -1);
		size_dfs(root), build_dfs(root);
	}
	template <class F>
	void each_edge(int u, int v, const F& func) const {
		while (true) {
			if (label[u] > label[v]) std::swap(u, v);
			if (head[u] == head[v]) {
				if (label[u] != label[v]) func(label[u] + 1, label[v]);
				return;
			}
			func(label[head[v]], label[v]);
			v = par[head[v]];
		}
	}
	template <class F>
	void each_vertex(int u, int v, const F& func) const {
		while (true) {
			if (label[u] > label[v]) std::swap(u, v);
			if (head[u] == head[v]) {
				func(label[u], label[v]);
				return;
			}
			func(label[head[v]], label[v]);
			v = par[head[v]];
		}
	}
	template <class F>
	void each_vertex_subtree(int u, const F& func) const {
		func(label[u], last[u]);
	}
	int lca(int u, int v) const {
		while (true) {
			if (label[u] > label[v]) std::swap(u, v);
			if (head[u] == head[v]) return u;
			v = par[head[v]];
		}
	}
	void clear() {
		vec.clear(), size.clear(), par.clear(), head.clear(), label.clear(), last.clear();
	}
};

/**
 * @title Heavy light decomposition
 */
#line 6 "test/yosupo/vertex_set_path_composite.test.cpp"
using ModInt = StaticModInt<998244353>;
using MP = std::pair<ModInt, ModInt>;
MP nodef(const MP& lhs, const MP& rhs) {
	return {lhs.first * rhs.first, lhs.second * rhs.first + rhs.second};
}
class MySeg : public SegTree<MP, nodef> {
	using Base = SegTree<MP, nodef>;

  public:
	MySeg(int n) : Base(n, MP{1, 0}, MP{1, 0}) {}
};
int n, q;
IP a[200010];
int main() {
	scanf("%d%d", &n, &q);
	rep(i, n) scanf("%d%d", &a[i].first, &a[i].second);
	HeavyLightDecomposition hld(n);
	MySeg st1(n), st2(n);
	rep(i, n - 1) {
		int u, v;
		scanf("%d%d", &u, &v);
		hld.add_edge(u, v);
	}
	hld.build(0);
	rep(i, n) {
		st1.update(hld.label[i], a[i]);
		st2.update(n - 1 - hld.label[i], a[i]);
	}
	rep(i, q) {
		int t;
		scanf("%d", &t);
		if (t == 0) {
			int p, c, d;
			scanf("%d%d%d", &p, &c, &d);
			a[p] = {c, d};
			st1.update(hld.label[p], {c, d});
			st2.update(n - 1 - hld.label[p], {c, d});
		} else {
			int u, v, x;
			scanf("%d%d%d", &u, &v, &x);
			int t = hld.lca(u, v);
			std::pair<ModInt, ModInt> f1(1, 0), f2(1, 0);
			hld.each_vertex(u, t, [&](int l, int r) {
				auto p = st2.query(n - 1 - r, n - 1 - l + 1);
				f1 = {f1.first * p.first, f1.second * p.first + p.second};
			});
			f1 = {f1.first / a[t].first,
				  (f1.second - a[t].second) / a[t].first};
			hld.each_vertex(t, v, [&](int l, int r) {
				auto p = st1.query(l, r + 1);
				f2 = {p.first * f2.first, p.second * f2.first + f2.second};
			});
			f1 = {f1.first * f2.first, f1.second * f2.first + f2.second};
			printf("%d\n", ModInt(x) * f1.first + f1.second);
		}
	}
}