hdu 3944 DP? (Lucas 定理)

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
const int maxn=10005;
int n,k,p;
int frc[1300][maxn];
int id[maxn];
bool vis[maxn];
int prim[maxn];
int cnt;
void init(){
    for(int i=2;i<maxn;i++)if(!vis[i]){
        prim[cnt]=i;
        id[i]=cnt;
        for(int j=i*2;j<maxn;j+=i)vis[j]=1;
        p=i;
        frc[cnt][0]=1;
        for(int j=1;j<p;j++)frc[cnt][j]=frc[cnt][j-1]*j%p;
        cnt++;
    }
}
int POW(int x,int n,int p){
    int res=1;
    while(n){
        if(n&1)res=res*x%p;
        x=x*x%p;
        n>>=1;
    }
    return res;
}
int cm(int n,int m,int p){
    if(m>n)return 0;
    int x=id[p];
    int ans=frc[x][n]*POW(frc[x][n-m]*frc[x][m]%p,p-2,p)%p;
    return ans;
}
int lucas(int n,int m,int p){
    if(m==0)return 1;
    int ans=cm(n%p,m%p,p)*lucas(n/p,m/p,p)%p;
    return ans;
}
int main()
{
//    freopen("in","r",stdin);
    init();
    int cas=1;
    while(scanf("%d%d%d",&n,&k,&p)>0){
        if(k>n/2)k=n-k;
        int ans=lucas(n+1,k,p)+n-k;
        printf("Case #%d: %d\n",cas++,ans%p);
    }
    return 0;
}