agc023C - Painting Machines(组合数)

#include<bits/stdc++.h>
#define LL long long 
using namespace std;
const int MAXN = 1e6 + 10, INF = 1e9 + 7, mod = 1000000007;
template<typename A, typename B> inline void chmax(A &x, B y) {
    x = x > y ? x : y;
}
template<typename A, typename B> inline void chmin(A &x, B y) {
    x = x < y ? x : y;
}
template<typename A, typename B> inline int mul(A x, B y) {
    return 1ll * x * y % mod;
}
template<typename A, typename B> inline void add2(A &x, B y) {
    if(x + y < 0) x = x + y + mod;
    else x = (x + y >= mod ? x + y - mod : x + y);
}
template<typename A, typename B> inline int add(A x, B y) {
    if(x + y < 0) return x + y + mod;
    else return x + y >= mod ? x + y - mod : x + y;
}
template<typename A, typename B> inline int fp(A a, B p) {
    int base = 1;
    while(p) {
        if(p & 1) base = mul(base, a);
        a = mul(a, a); p >>= 1;
    }
    return base;
}
inline int read() {
    char c = getchar(); int x = 0, f = 1;
    while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();}
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
    return x * f;
}
int N, fac[MAXN], ifac[MAXN], f[MAXN];
int C(int N, int M) {
    if(M > N) return 0;
    return mul(fac[N], mul(ifac[M], ifac[N - M]));
}
int main() {
    N = read(); fac[0] = 1;
    for(int i = 1; i <= N; i++) fac[i] = mul(i, fac[i - 1]);
    ifac[N] = fp(fac[N], mod - 2);
    for(int i = N; i >= 1; i--) ifac[i - 1] = mul(ifac[i], i);
    int down = N / 2 + (N & 1);
    for(int i = down; i < N; i++) 
        f[i] = mul(mul(C(i - 1, N - i - 1), fac[i]), fac[N - i - 1]);
    int ans = 0;
    for(int i = down; i < N; i++) add2(ans, mul(i, add(f[i], -f[i - 1])));
    cout << ans;
    return 0;
}
/*
3
0 1 1
5 7 3
*/