BZOJ 2111 [ZJOI2010]Perm 排列计数

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
typedef long long Lint;
const int maxn=1000009;

int n,mm;

Lint f[maxn];
int h[maxn];
Lint g[maxn];
Lint Ksm(Lint a,int p){
	Lint ret=1;
	for(;p;p>>=1,a=a*a%mm){
		if(p&1)ret=ret*a%mm;
	}
	return ret;
}
Lint Inv(Lint x){
	return Ksm(x,mm-2);
}
Lint C(int n,int m){
	int tmp=h[n]-h[m]-h[n-m];
	if(tmp)return 0;
	return f[n]*Inv(f[m])%mm*Inv(f[n-m])%mm;
}

int t=0;
int main(){
	scanf("%d%d",&n,&mm);
	f[0]=1;h[0]=0;
	for(int i=1;i<=n;++i){
		int x=i;h[i]=h[i-1];
		while(x%mm==0){
			x/=mm;++h[i];
		}
		f[i]=f[i-1]*x%mm;
	}
	
	g[0]=g[1]=1;
	for(int i=2;i<=n;++i){
		while((1<<(t+1))-1<=i)++t;
		int res=i-((1<<t)-1);
		if(res>=(1<<(t-1))){
			g[i]=C(i-1,(1<<t)-1)*g[(1<<t)-1]%mm*g[i-(1<<t)]%mm;
		}else{
			g[i]=C(i-1,(1<<(t-1))+res-1)*g[(1<<(t-1))+res-1]%mm*g[(1<<(t-1))-1]%mm;
		}
	}
	cout<<g[n]<<endl;
}