[ZJOI2010]排列计数

#include<iostream>
#include<cstdio>
using namespace std;
typedef long long ll;
const int N=2e6+10;
ll ni[N],jie[N],n,p,cnt[N],dp[N],x;
inline ll C(int n,int m){
   if(n<=x)return jie[n]*ni[m]%p*ni[n-m]%p;
   else return C(n/p,m/p)*C(n%p,m%p)%p;
}
inline ll power(ll x,ll y){
    ll ans=1;
    while(y){
        if(y&1)ans=ans*x%p;x=x*x%p;y>>=1;
    }
    return ans;
}
int main(){
    cin>>n>>p;
    jie[0]=1;
    x=min(n,p-1);
    for(int i=1;i<=x;++i)jie[i]=jie[i-1]*i%p;ni[x]=power(jie[x],p-2);
    for(int i=x-1;i>=0;--i)ni[i]=ni[i+1]*(i+1)%p;
    for(int i=n;i>=1;--i){
        cnt[i]++;cnt[i/2]+=cnt[i];
        if(i*2>n)dp[i*2]=1;
        if(i*2+1>n)dp[i*2+1]=1;
        dp[i]=C(cnt[i]-1,cnt[i*2])*dp[i*2]%p*dp[i*2+1]%p;
    }
    cout<<dp[1];
    return 0;
}