组合数+容斥原理 UVALive 7040 Color(14西安F)

#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <iostream>
#include <vector>
#include <set>
#include <map>
#include <queue>
using namespace std;

#define lson l, mid, rt << 1
#define rson mid + 1, r, rt << 1 | 1
typedef long long ll;
const int N = 1e6 + 10;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 7;
const int EPS = 1e-8;
int inv[N];

void init(int n)	{
	inv[1] = 1;
	for (int i=2; i<=n; ++i)	{
		inv[i] = (MOD - MOD / i) * 1ll * inv[MOD%i] % MOD;		//inv[n]
	}
}

int pow_mod(int x, int n, int p)	{
	int ret = 1;
	while (n)	{
		if (n & 1)	ret = ret * 1l * x % p;
        x = x * 1ll * x % p;
        n >>= 1;
	}
	return ret;
}

int f(int n, int k)	{
	if (!k)	return 0;
	else	return k * 1ll * pow_mod (k-1, n-1, MOD) % MOD;
}

int main(void)	{
	init (1000000);
	int T, cas = 0;	scanf ("%d", &T);
	while (T--)	{
		int n, m, k;	scanf ("%d%d%d", &n, &m, &k);
		ll ans = 0;	int res = 1;
		for (int i=1; i<=k; ++i)	{
			res = res * 1ll * (k - i + 1) % MOD * inv[i] % MOD;
			if (k - i & 1)	{
				ans -= res * 1ll * f (n, i) % MOD;
				if (ans < 0)	ans += MOD;
			}
			else	{
				ans += res * 1ll * f (n, i) % MOD;
				if (ans >= MOD)	ans -= MOD;
			}
		}
		for (int i=1; i<=k; ++i)	{
			ans = ans * 1ll * (m - i + 1) % MOD * inv[i] % MOD;
		}
		printf ("Case #%d: %lld\n", ++cas, ans);
	}

	return 0;
}