1 #include<cstdio>
 2 typedef long long LL;
 3 int n, flag;
 4 LL fac[25];
 5 LL ans;
 6 void init(){
 7     fac[0] = 1;
 8     for(int i = 1; i <= 20; i ++) fac[i] = fac[i-1] * i;
 9 }
10 int main(){
11     init();
12     while(~scanf("%d", &n)){
13         ans = 0;
14         flag = n & 1 ? -1 : 1;//起始符号
15         for(int i = 0; i <= n; i ++){
16             ans += flag * fac[n] / fac[n-i];
17             flag = -flag;
18         }
19         printf("%I64d\n", ans);
20     }
21 }

 1 #include<cstdio>
 2 typedef long long LL;
 3 const int N = 1000000 + 5;
 4 const int MOD = (int)1e9 + 7;
 5 int F[N], Finv[N], inv[N];
 6 LL pow_mod(LL a, LL b, LL p){
 7     LL ret = 1;
 8     while(b){
 9         if(b & 1) ret = (ret * a) % p;
10         a = (a * a) % p;
11         b >>= 1;
12     }
13     return ret;
14 }
15 void init(){
16     inv[1] = 1;
17     for(int i = 2; i < N; i ++){
18         inv[i] = (MOD - MOD / i) * 1ll * inv[MOD % i] % MOD;
19     }
20     F[0] = Finv[0] = 1;
21     for(int i = 1; i < N; i ++){
22         F[i] = F[i-1] * 1ll * i % MOD;
23         Finv[i] = Finv[i-1] * 1ll * inv[i] % MOD;
24     }
25 }
26 int comb(int n, int m){
27     if(m < 0 || m > n) return 0;
28     return F[n] * 1ll * Finv[n - m] % MOD * Finv[m] % MOD;
29 }
30 int main(){
31     init();
32     int T, n, m, k, ans, flag, temp;
33     scanf("%d", &T);
34     for(int cas = 1; cas <= T; cas ++){
35         scanf("%d%d%d", &n, &m, &k);
36         ans = 0;
37         flag = (k & 1) ? 1 : -1;
38         //计算g(k)
39         for(int i = 1; i <= k; i ++){
40             ans = (ans + 1ll * flag * comb(k, i) * i % MOD * pow_mod(i-1, n-1, MOD) % MOD) % MOD;
41             flag = -flag;
42         }
43         //接下来计算C(m, k)
44         temp = Finv[k];
45         for(int i = 1; i <= k; i ++){
46             temp = 1ll * temp * (m-k+i) % MOD;
47         }
48         ans = ((1ll * ans * temp) % MOD + MOD) % MOD;
49         printf("Case #%d: %d\n", cas, ans);
50     }
51 }