結果

問題 No.187 中華風 (Hard)
コンテスト
ユーザー heno239
提出日時 2020-08-14 14:17:50
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 5,435 bytes
コンパイル時間 1,553 ms
コンパイル使用メモリ 130,904 KB
実行使用メモリ 20,044 KB
最終ジャッジ日時 2024-10-10 11:53:58
合計ジャッジ時間 5,515 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
other AC * 24 WA * 1
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ソースコード

diff # 

#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acos(-1.0);

ll mod_pow(ll x, ll n, ll m = mod) {
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n % mod + mod) % mod;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }

const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}

ll gcd(ll a, ll b) {
	if (a < b)swap(a, b);
	while (b) {
		ll r = a % b; a = b; b = r;
	}
	return a;
}

//x,yがax+by=gcd(a,b)の解になる
ll extgcd(ll a, ll b, ll& x, ll& y) {
	ll d = a;
	if (b != 0) {
		d = extgcd(b, a % b, y, x);
		y -= (a / b) * x;
	}
	else {
		x = 1; y = 0;
	}
	return d;
}
//aのmod mでの逆元を求める
ll mod_inverse(ll a, ll m) {
	ll x, y;
	extgcd(a, m, x, y);
	return (m + x % m) % m;
}

bool isp[40000];
vector<int> ps;
void init() {
	fill(isp + 2, isp + 40000, true);
	for (int i = 2; i * i <= 1000000000; i++) {
		if (!isp[i])continue;
		ps.push_back(i);
		for (int j = 2 * i; j < 40000; j += i) {
			isp[j] = false;
		}
	}
}
void solve() {
	int n; cin >> n;
	vector<pair<P, int>> vs;
	rep(i, n) {
		int x, y; cin >> x >> y;
		int cop = y;
		for (int p : ps) {
			if (cop % p == 0) {
				int cnt = 0; int s = 1;
				while (cop % p == 0) {
					cnt++; cop /= p;
					s *= p;
				}
				vs.push_back({ {p,cnt},x % s });
			}
		}
		if (cop > 1) {
			vs.push_back({ {cop,1},x % cop });
		}
	}
	sort(all(vs));

	vector<P> vr;
	vr.push_back({ 1,0 });
	rep(i, vs.size()) {
		int le = i;
		while (i + 1 < vs.size() && vs[i].first.first == vs[i + 1].first.first) {
			i++;
		}
		for (int j = le + 1; j <= i; j++) {
			int dif = vs[j].first.second - vs[j - 1].first.second;
			if (dif == 0) {
				if (vs[j].second != vs[j - 1].second) {
					cout << -1 << "\n"; return;
				}
			}
			else {
				int x = 1;
				rep(k, dif)x *= vs[j].first.first;
				int r = vs[j].second - vs[j - 1].second;
				if (r % x) {
					cout << -1 << "\n"; return;
				}
			}
		}
		int x = 1;
		rep(k, vs[i].first.second)x *= vs[i].first.first;
		vr.push_back({ x,vs[i].second });
	}
	sort(all(vr));
	bool exi = false;
	rep(i, vr.size()) {
		if (vr[i].second > 0)exi = true;
	}
	if (!exi) {
		modint ans = 1;
		rep(i, vr.size()) {
			ans*=vr[i].first;
		}
		cout << ans << "\n"; return;
	}
	int len = vr.size();
	vector<ll> memo(len);
	vector<ll> memo2(len);
	memo[0] = vr[1].second;
	memo2[0] = 0;
	//rep(i, len)cout << vr[i].first << " " << vr[i].second << "\n";
	for (int i = 1; i < len - 1; i++) {
		//memo[i]
		ll s = 0;
		ll z = 1;
		for (int j = 0; j < i; j++) {
			z = z * vr[j].first % vr[i + 1].first;
			s = (s + memo[j] * z) % vr[i + 1].first;
		}
		//cout << "? " << i << " " << s << "\n";
		memo[i] = vr[i + 1].second - s; if (memo[i] < 0)memo[i] += vr[i + 1].first;

		//cout << z << "\n";
		rep(j, i + 1) {
			memo[i] = memo[i] * mod_inverse(vr[j].first, vr[i + 1].first) % vr[i + 1].first;
		}
	}
	//rep(i, len - 1)cout << memo[i] << "\n";
	ll ans = 0;
	ll z = 1;
	for (int i = 0; i < len - 1; i++) {
		z = z * vr[i].first % mod;
		ans = (ans + memo[i] * z) % mod;
	}
	cout << ans << "\n";
}





signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	//init_f();
	init();
	//expr();
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}
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