kickstart_2018_round_H_C Let Me Count The Ways

思路：

容斥。

实现：

 #include <bits/stdc++.h>
 using namespace std;
 typedef long long ll;
 const ll MOD = 1e9 + ;
 const int MAXN = ;
 ll f[MAXN + ], inv[MAXN + ];
 ll pow(ll a, ll b)
 {
     ll res = ;
     while (b)
     {
         if (b & )
             res = res * a % MOD;
         b >>= ;
         a = a * a % MOD;
     }
     return res;
 }

 void init()
 {
     f[] = ;
     for (int i = ; i <= MAXN; i++) f[i] = f[i - ] * i % MOD;
     inv[MAXN] = pow(f[MAXN], MOD - );
     for (int i = MAXN - ; i >= ; i--) inv[i] = inv[i + ] * (i + ) % MOD;
 }

 ll C(int a, int b)
 {
     return f[a] * inv[b] % MOD * inv[a - b] % MOD;
 }

 int main()
 {
     init();
     int T, n, m;
     cin >> T;
     for (int i = ; i <= T; i++)
     {
         cin >> n >> m;
         ll ans = , s = , bin = ;
         for (int i = ; i <= m; i++)
         {
             ans = (ans + s * C(m, i) * bin % MOD * f[ * n - i] % MOD) % MOD;
             s *= -;
             bin = bin *  % MOD;
         }
         cout << "Case #" << i << ": " << (ans + MOD) % MOD << endl;
     }
     return ;
 }