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 + 7;
const int MAXN = 200000;
ll f[MAXN + 5], inv[MAXN + 5];
ll pow(ll a, ll b)
{
    ll res = 1;
    while (b)
    {
        if (b & 1)
            res = res * a % MOD;
        b >>= 1;
        a = a * a % MOD;
    }
    return res;
}

void init()
{
    f[0] = 1;
    for (int i = 1; i <= MAXN; i++) f[i] = f[i - 1] * i % MOD;
    inv[MAXN] = pow(f[MAXN], MOD - 2);
    for (int i = MAXN - 1; i >= 0; i--) inv[i] = inv[i + 1] * (i + 1) % 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 = 1; i <= T; i++)
    {
        cin >> n >> m;
        ll ans = 0, s = 1, bin = 1;
        for (int i = 0; i <= m; i++)
        {
            ans = (ans + s * C(m, i) * bin % MOD * f[2 * n - i] % MOD) % MOD;
            s *= -1;
            bin = bin * 2 % MOD;
        }
        cout << "Case #" << i << ": " << (ans + MOD) % MOD << endl;
    }
    return 0;
}