結果

問題 No.125 悪の花弁
ユーザー heno239
提出日時 2020-08-04 23:40:28
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 57 ms / 5,000 ms
コード長 3,930 bytes
コンパイル時間 1,163 ms
コンパイル使用メモリ 117,296 KB
実行使用メモリ 32,772 KB
最終ジャッジ日時 2024-09-14 23:32:03
合計ジャッジ時間 2,118 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge6
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ファイルパターン 結果
other AC * 6
権限があれば一括ダウンロードができます

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 long 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) {
	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, int 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];
}
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };

const int mn = 1000000;
int id[mn + 1];
bool isp[mn + 1];
void init() {
	fill(id, id + mn + 1, 1);
	fill(isp + 2, isp + mn + 1, true);
	for (int i = 2; i <= mn; i++) {
		if (!isp[i])continue;
		id[i] *= -1;
		for (int j = 2 * i; j <= mn; j += i) {
			isp[j] = false;
			id[j] *= -1;
			if ((j / i) % i == 0) {
				id[j] = 0;
			}
		}
	}
}
void solve(){
	init();
	//rep1(i, 50)cout << i << " " << id[i] << "\n";
	int n; cin >> n;
	vector<int> c(n);
	rep(i, n)cin >> c[i];
	int sum = 0;
	rep(i, n)sum += c[i];

	modint pro = 1;
	int cur = sum - c[0];
	rep1(i, n - 1) {
		pro *= comb(cur, c[i]);
		cur -= c[i];
	}


	vector<int> ds;
	vector<modint> memo(sum + 1);

	modint ans = 0;
	for (int b = 1; b <= sum; b++) {
		if (sum % b)continue;
		int d = sum / b;

		bool valid = true;
		rep(i, n)if (c[i] % d) {
			valid = false; break;
		}
		if (!valid)continue;

		memo[b] = fact[sum / d];
		rep(i, n) {
			memo[b] *= factinv[c[i] / d];
		}
		
		modint x = memo[b];
		for (int p : ds) {
			if (b % p == 0) {
				x += (modint)id[b / p] * memo[p];
			}
		}

		ds.push_back(b);
		
		//cout << b << " " << memo[b] << "\n";
		x = x / (modint)b;
			ans += x;
	}
	cout << ans << "\n";
}






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