牛客OI周赛4-提高组 B 最后的晚餐(dinner)

最后的晚餐(dinner)

思路:

容斥

求 ∑(-1)^i * C(n, i) * 2^i * (2n-i-1)!

这道题卡常数

#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize(4)
#include<bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define pi acos(-1.0)
#define LL long long
//#define mp make_pair
#define pb push_back
#define ls rt<<1, l, m
#define rs rt<<1|1, m+1, r
#define ULL unsigned LL
#define pll pair<LL, LL>
#define pli pair<LL, int>
#define pii pair<int, int>
#define piii pair<pii, int>
#define mem(a, b) memset(a, b, sizeof(a))
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define fopen freopen("in.txt", "r", stdin);freopen("out.txt", "w", stout);
//head

const LL MOD = 1e9 + 7;
const int N = 3e7 + 5;
int f[N], inv[N];
LL q_pow(LL n, LL k) {
    LL ans = 1;
    while(k) {
        if(k&1) ans = (ans * n) % MOD;
        n = (n * n) % MOD;
        k >>= 1;
    }
    return ans;
}
int main() {
    int n;
    scanf("%d", &n);
    if(n == 1) return 0*puts("0");
    LL ans = 0;
    int fac = 1, pw = q_pow(2, n), c = 1;
    f[0] = 1;
    for (int i = 1; i <= n; i++) f[i] = (1LL * f[i-1] * i) % MOD;
    inv[n] = q_pow(f[n], MOD-2) % MOD;
    for (int i = n-1; i >= 0; i--) inv[i] = (1LL * inv[i+1]*(i+1)) % MOD;
    fac = f[n-1];
    for (int i = n; i >= 0; i--) {
        (ans += ((i%2) ? -1 : 1) * 1LL * inv[i] % MOD * inv[n-i] % MOD * pw % MOD * fac) %= MOD;
        fac = (1LL * fac * (2*n - i)) % MOD;
        pw = (1LL * pw * inv[2]) % MOD;
    }
    ans = (ans + MOD) % MOD;
    ans = ans * f[n] % MOD;
    printf("%lld\n", ans);
    return 0;
}