BZOJ 1485: [HNOI2009]有趣的数列

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int N=100000+5;
const int M=2000000+5;
bool is[M];
int p[M],tot,cnt[M],mi[M],n;
void sieve(){
for(int i=2;i<=2*n;i++){
if(!is[i])p[++tot]=i,mi[i]=tot;
for(int j=1;j<=tot&&p[j]*i<=2*n;j++){
is[p[j]*i]=1;mi[p[j]*i]=j;
if(i%p[j]==0)break;
}
}
}
void depart(int x,int v){
while(x>1){
cnt[mi[x]]+=v;
x/=p[mi[x]];
}
}
void C(int n,int m){
for(int i=n;i>m;i--)depart(i,1);
for(int i=1;i<=n-m;i++)depart(i,-1);
}
typedef long long ll;
ll qmul(ll a,ll b,ll P){
ll ans=1;
for(;b;b>>=1,a=a*a%P)if(b&1)ans=ans*a%P;
return ans;
}
int main(){
//freopen("a.in","r",stdin);
int P;scanf("%d%d",&n,&P);
sieve();
C(2*n,n);depart(n+1,-1);
ll ans=1;
for(int i=1;i<=tot;i++)
if(cnt[i])ans=ans*qmul(p[i],cnt[i],P)%P;//printf("%d %d\n",p[i],cnt[i]);
printf("%lld\n",ans);
return 0;
}