#1196147 (C++23) No.3785 Tree of Multiples

• 問題: No.3785 Tree of Multiples
• ユーザー: shobonvip
• 提出日時: 2026-10-30 23:15:37
• 言語: C++23 (gcc 15.3.0 + boost 1.92.0 + ACL)
• 結果: AC
• 実行時間: 1,127 ms / 6,000 ms
• コード長: 4,997 bytes
• コンパイル時間: 6,542 ms
• コンパイル使用メモリ: 404,252 KB
• 実行使用メモリ: 64,740 KB
• 最終ジャッジ日時: 2026-10-30 23:16:02
• 合計ジャッジ時間: 14,714 ms
• ジャッジサーバーID （参考情報）: judge4_0 / judge1_0

ファイルパターン	結果
sample	AC * 3
other	AC * 16

ソースコード

/**
	author:  shobonvip
	created: 2026.10.30 22:42:40
**/

#include<bits/stdc++.h>
using namespace std;

//* ATCODER
#include<atcoder/all>
using namespace atcoder;
typedef modint998244353 mint;
//*/

/* BOOST MULTIPRECISION
#include<boost/multiprecision/cpp_int.hpp>
using namespace boost::multiprecision;
//*/

typedef long long ll;

#define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++)
#define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--)
#define all(v) v.begin(), v.end()

template <typename T> bool chmin(T &a, const T &b) {
	if (a <= b) return false;
	a = b;
	return true;
}

template <typename T> bool chmax(T &a, const T &b) {
	if (a >= b) return false;
	a = b;
	return true;
}

template <typename T> T max(vector<T> &a){
	assert(!a.empty());
	T ret = a[0];
	for (int i=0; i<(int)a.size(); i++) chmax(ret, a[i]);
	return ret;
}

template <typename T> T min(vector<T> &a){
	assert(!a.empty());
	T ret = a[0];
	for (int i=0; i<(int)a.size(); i++) chmin(ret, a[i]);
	return ret;
}

template <typename T> T sum(vector<T> &a){
	T ret = 0;
	for (int i=0; i<(int)a.size(); i++) ret += a[i];
	return ret;
}

//defmodfact
const int COMinitMAX = 999999;
mint fact[COMinitMAX+1], factinv[COMinitMAX+1];

void modfact(){
	fact[0] = 1;
	for (int i=1; i<=COMinitMAX; i++){
		fact[i] = fact[i-1] * i;
	}
	factinv[COMinitMAX] = fact[COMinitMAX].inv();
	for (int i=COMinitMAX-1; i>=0; i--){
		factinv[i] = factinv[i+1] * (i+1);
	}
}

mint cmb(int a, int b){
	if (a<b || b<0) return mint(0);
	return fact[a]*factinv[b]*factinv[a-b];
}
//--------

struct S {
	vector<mint> v[4];
};

int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	
	// FPS game

	modfact();
	int n, m;
	cin >> n >> m;
	map<ll,ll> mp_a;
	map<ll,ll> mp_b;
	ll sum_a = 0, sum_b = 0;
	rep(i,0,n) {
		ll p,a; cin >> p >> a;
		mp_a[p] = a;
		sum_a += a;
	}
	rep(i,0,m) {
		ll q,b; cin >> q >> b;
		mp_b[q] = b;
		sum_b += b;
	}

	// 倍数関係にある場合, だめだったw

	bool a_div_b = true, b_div_a = true;
	for (auto [p,a]: mp_a) {
		if (!mp_b.contains(p) || mp_b[p] < a) {
			a_div_b = false;
			break;
		}
	}
	for (auto [q,b]: mp_b) {
		if (!mp_a.contains(q) || mp_a[q] < b) {
			b_div_a = false;
			break;
		}
	}

	mint ans = 0;

	if (a_div_b) {
		mint tmp = fact[sum_a];
		for (auto [p,a]: mp_a) {
			tmp *= factinv[a];
			tmp *= mint(p).pow(a);
		}
		tmp *= fact[sum_b-sum_a];
		for (auto [q,b]: mp_b) {
			if (mp_a.contains(q)) tmp *= factinv[b-mp_a[q]];
			else tmp *= factinv[b];
		}
		ans += tmp;
	}
	
	if (b_div_a && !a_div_b) {
		mint tmp = fact[sum_b];
		for (auto [q,b]: mp_b) {
			tmp *= factinv[b];
			tmp *= mint(q).pow(b);
		}
		tmp *= fact[sum_a-sum_b];
		for (auto [p,a]: mp_a) {
			if (mp_b.contains(p)) tmp *= factinv[a-mp_b[p]];
			else tmp *= factinv[a];
		}
		ans += tmp;
	}
	

	deque<S> f;
	
	map<ll,ll> mp_gcd;
	for (auto [p,a]: mp_a) {
		if (mp_b.contains(p)) {
			ll b = mp_b[p];
			ll t = min(a, b);
			mp_gcd[p] = min(a,b);
			S tmp;
			tmp.v[0].resize(t+1);
			tmp.v[1].resize(t+1);
			tmp.v[2].resize(t+1);
			tmp.v[3].resize(t+1);
			mint art=1;

			rep(i,0,t+1) {
				tmp.v[0][i] = art*factinv[i]*factinv[a-i]*factinv[b-i];
				if (a-i>0) {
					tmp.v[1][i] = art*factinv[i]*factinv[a-i-1]*factinv[b-i];
				}
				if (b-i>0) {
					tmp.v[2][i] = art*factinv[i]*factinv[a-i]*factinv[b-i-1];
				}
				art*=p;
			}

			f.emplace_back(tmp);
		} else {
			S tmp;
			tmp.v[0].resize(1);
			tmp.v[1].resize(1);
			tmp.v[2].resize(1);
			tmp.v[3].resize(1);

			tmp.v[0][0] = factinv[a];
			tmp.v[1][0] = factinv[a] * a;
			f.emplace_back(tmp);
		}
	}

	for (auto [q,b]: mp_b) {
		if (!mp_a.contains(q)) {
			S tmp;
			tmp.v[0].resize(1);
			tmp.v[1].resize(1);
			tmp.v[2].resize(1);
			tmp.v[3].resize(1);

			tmp.v[0][0] = factinv[b];
			tmp.v[2][0] = factinv[b] * b;
			f.emplace_back(tmp);
		}
	}

	while(f.size()>1) {
		S f1 = f.front(); f.pop_front();
		S f2 = f.front(); f.pop_front();

		vector<mint> g00 = convolution(f1.v[0], f2.v[0]);

		vector<mint> g01 = convolution(f1.v[0], f2.v[1]);
		vector<mint> g10 = convolution(f1.v[1], f2.v[0]);

		vector<mint> g02 = convolution(f1.v[0], f2.v[2]);
		vector<mint> g20 = convolution(f1.v[2], f2.v[0]);

		vector<mint> g03 = convolution(f1.v[0], f2.v[3]);
		vector<mint> g30 = convolution(f1.v[3], f2.v[0]);

		vector<mint> g12 = convolution(f1.v[1], f2.v[2]);
		vector<mint> g21 = convolution(f1.v[2], f2.v[1]);

		int sz = (int)g00.size();
		S tmp;
		tmp.v[0].resize(sz);
		tmp.v[1].resize(sz);
		tmp.v[2].resize(sz);
		tmp.v[3].resize(sz);
		rep(i,0,sz) {
			tmp.v[0][i] += g00[i];
			tmp.v[1][i] += g01[i];
			tmp.v[1][i] += g10[i];
			tmp.v[2][i] += g02[i];
			tmp.v[2][i] += g20[i];
			tmp.v[3][i] += g03[i];
			tmp.v[3][i] += g30[i];
			tmp.v[3][i] += g12[i];
			tmp.v[3][i] += g21[i];
		}
		f.emplace_back(tmp);
	}

	rep(i,0,(int)f[0].v[3].size()) {
		if (sum_a-i-1 >= 0 && sum_b-i-1 >= 0) {
			ans += f[0].v[3][i] * fact[i] * fact[sum_a-i-1] * fact[sum_b-i-1];
		}
	}

	cout << ans.val() << endl;






}