洛谷P2606 [ZJOI2010]排列计数(组合数 dp)

#include<cstdio>
//#define int long long 
using namespace std;
const int MAXN = 1e6 + 10;
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, P, fac[MAXN] = {1}, ifac[MAXN], siz[MAXN], f[MAXN];
int fastpow(int a, int p, int mod) {
    int base = 1;
    while(p) {
        if(p & 1) base = (1ll * base % mod * a % mod) % mod;
        a = (1ll * a % mod * a % mod) % mod; p >>= 1;
    }
    return base % mod;
}
int C(int N, int M, int P) {
    if(M > N) return 0;
    return 1ll * fac[N] % P * ifac[M] % P * ifac[N - M] % P;
}
int Lucas(int N, int M, int P) {
    if(!N || !M) return 1;
    return Lucas(N / P, M / P, P) * C(N % P, M % P, P);    
}
main() {
    N = read(); P = read();
    for(int i = 1; i <= N; i++) fac[i] = 1ll * i * fac[i - 1] % P;
    ifac[N] = fastpow(fac[N], P - 2, P);
    for(int i = N; i >= 1; i--) ifac[i - 1] = 1ll * i * ifac[i] % P;
    for(int i = N; i >= 1; i--) {
        siz[i] = 1;
        int ls = (i << 1), rs = (i << 1 | 1);
        if(rs <= N) siz[i] += siz[ls] + siz[rs], f[i] = 1ll * Lucas(siz[i] - 1, siz[ls], P) * f[ls] % P * f[rs] % P;    
        else if(ls <= N) siz[i] += siz[ls], f[i] = f[ls];
        else f[i] = 1;
    }
    printf("%d", f[1]);
    return 0;
}
/*
999999 1000000007
*/