#242762 (C++14) No.665 Bernoulli Bernoulli

• 問題: No.665 Bernoulli Bernoulli
• ユーザー: polylogK
• 提出日時: 2018-03-09 23:16:22
• 言語: C++14 (gcc 13.2.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 369 ms / 2,000 ms
• コード長: 2,193 bytes
• コンパイル時間: 1,863 ms
• コンパイル使用メモリ: 164,748 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-04-19 02:30:29
• 合計ジャッジ時間: 8,200 ms
• ジャッジサーバーID （参考情報）: judge2 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	3 ms; 5,248 KB
testcase_01	AC	4 ms; 5,376 KB
testcase_02	AC	369 ms; 5,376 KB
testcase_03	AC	366 ms; 5,376 KB
testcase_04	AC	337 ms; 5,376 KB
testcase_05	AC	323 ms; 5,376 KB
testcase_06	AC	311 ms; 5,376 KB
testcase_07	AC	301 ms; 5,376 KB
testcase_08	AC	306 ms; 5,376 KB
testcase_09	AC	343 ms; 5,376 KB
testcase_10	AC	309 ms; 5,376 KB
testcase_11	AC	357 ms; 5,376 KB
testcase_12	AC	345 ms; 5,376 KB
testcase_13	AC	358 ms; 5,376 KB
testcase_14	AC	364 ms; 5,376 KB
testcase_15	AC	318 ms; 5,376 KB
testcase_16	AC	325 ms; 5,376 KB
testcase_17	AC	314 ms; 5,376 KB
testcase_18	AC	302 ms; 5,376 KB

ソースコード

#include <bits/stdc++.h>
#define pq priority_queue
#define P pair<int, int>
#define P2 pair<int, P>
#define P3 pair<int, P2>
using namespace std;
typedef long long ll; typedef long double ld;
constexpr long long gcd(long long a, long long b){return b ? gcd(b, a % b) : a;}
constexpr long long lcm(long long a, long long b){return a / gcd(a, b) * b;}
constexpr int INF = 1e9, MOD = INF + 7, around[] = {0, 1, 1, -1, -1, 0, -1, 1, 0, 0};
constexpr int mod_pow(long long x, long long n, const int mod){long long ret=1;while(n){if(n&1)(ret*=x)%=mod;(x*=x)%=mod;n>>=1;}return ret;}
template<int n> struct Prime{bool arr[n+1];constexpr bool operator[](int k){return arr[k];}constexpr Prime():arr(){for(int i=2;i<n;i++){arr[i]=true;for(int j=2;j*j<=i;j++){if(!(i%j))arr[i]=false;}}}};
template<int n> struct Factorial{long long arr[n+1],ary[n+1];constexpr Factorial():arr(),ary(){arr[0]=1;ary[0]=1;for(int i=0;i<n;i++){arr[i+1]=arr[i]*(i+1)%MOD;ary[i+1]=mod_pow(arr[i+1],MOD-2,MOD);}}};
//constexpr Factorial<10> fact;
constexpr Prime<10> prime;
//constexpr int comb(int a, int b){long long pos = fact.arr[a], pot = fact.ary[a - b], por = fact.ary[b];return pos * pot % MOD * por % MOD;}
constexpr int vx[] = {1, 0, -1, 0}, vy[] = {0, 1, 0, -1};
constexpr int sqrtN = 512, logN = 32;
constexpr ld PI = abs(acos(-1));
constexpr ll LINF=1e18;

ll b[10010], fact[10010], inv[10010];

void make(int n){
	fact[0] = inv[0] = 1;
	for(int i = 0; i < n; i++) fact[i + 1] = fact[i] * (i + 1) % MOD;
	for(int i = 0; i < n; i++) inv[i + 1] = mod_pow(fact[i + 1], MOD - 2, MOD);
}

ll comb(int a, int b){
	ll p = fact[a];
	ll q = inv[a - b];
	ll r = inv[b];
	
	return p * q % MOD * r % MOD;
}

int main(){
	ll n, k; cin >> n >> k;
	make(10010);
	
	b[0] = 1;
	for(int i = 1; i <= k + 1; i++){
		ll pos = 0;
		for(int j = 0; j < i; j++){
			(pos += comb(i + 1, j) * b[j] % MOD) %= MOD;
		}
		
		b[i] = (MOD - mod_pow(i + 1, MOD - 2, MOD)) % MOD * pos % MOD;
	}
	
	ll ans = 0; n++;
	for(int j = 0; j <= k; j++){
		ll p = comb(k + 1, j);
		ll q = b[j];
		ll r = mod_pow(n % MOD, k + 1 - j, MOD);
		
		(ans += p * q % MOD * r % MOD) %= MOD;
	}
	
	cout << ans * mod_pow(k + 1, MOD - 2, MOD) % MOD << endl;
	return 0;
}