Submission #995225

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Source Code Expand

#include<bits/stdc++.h>

using namespace std;
typedef long long int64;
const int mod = 1e9 + 7;

inline int64 modPow(int64 x, int64 n)
{
  if(n == 0) return (1);
  int64 ret = modPow(x, n / 2);
  (ret *= ret) %= mod;
  if(n & 1) (ret *= x) %= mod;
  return (ret);
}

inline int64 modInv(int64 a)
{
  return (modPow(a, mod - 2));
}

inline int64 modCombination(int p, int q)
{
  static int64 fact[202020], rfact[202020];
  if(fact[0] == 0) {
    fact[0] = rfact[0] = 1;
    for(int i = 1; i < 102020; i++) {
      fact[i] = fact[i - 1] * i % mod;
      rfact[i] = modInv(fact[i]);
    }
  }
  if(q < 0 || p < q) return (0);
  return (fact[p] * rfact[q] % mod * rfact[p - q] % mod);
}

inline int64 count1_3(int n, int k)
{
  if(n < k) return (0);
  int64 ret = 0;
  for(int i = 1; i <= k; i++) {
    // i 個以下の箱に n 個の玉を入れる場合の数
    int64 tmp = modCombination(k, i) * modPow(i, n) % mod;
    if((k - i) & 1) ret = (ret - tmp + mod) % mod;
    else (ret += tmp) %= mod;
  }
  return (ret);
}

inline int64 modFact(int n)
{
  int64 ret = 1;
  while(n > 1) (ret *= n--) %= mod;
  return (ret);
}

inline int64 count2_3(int n, int k)
{
  if(n < k) return (0);
  return (count1_3(n, k) * modInv(modFact(k)) % mod);
}

int main()
{
  int N, K;
  cin >> K >> N;
  cout << count2_3(N, K) << endl;
}

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