（1）楊輝三角

#include<iostream>
#include<cstdio>
#include<cmath>
#include<map>
#include<queue>
#include<algorithm>
#include<cstring>
#include<string>
using namespace std;
unsigned long long bj[2005][2005],c[2005][2005],z[2005][2005];
int k;
inline int read(){
    int s=0
 
,w=1;
    char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')w=-1;ch=getchar();}
    while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
    return s*w;
}
int init(){
    for(int i=0;i<=2000;i++) c[i][0]=c[i][i]=1;
    for(int i=1;i<=2000;i++)
        for(int j=1;j<=i;j++){
        c[i][j]
 
=(c[i-1][j]+c[i-1][j-1])%k;
        }
    return 0;
}
int main(){
    ios::sync_with_stdio(false);
    int T=read(); 
    k=read();
    init();
    while(T--){
        int x=read(),y=read();
        cout<<c[x][y]<<'\n';
    }
    return 0;
}

（2）Lucas定理

#include<iostream>
#include<cstdio>
const
 
 int MOD=2013;
int jc[MOD+5];
int gcd(int a,int b){
    if(b==0) return a;
    else return gcd(b,a%b);
}
int x,y;
void Extended_gcd(int a,int b){
    if(b==0){
        x=1;
        y=0;
    }
    else{
        Extended_gcd(b,a%b);
        long t=x;
        x=y;
        y=t-(a/b)*y;
    }
}
int C(int a,int b){
    if(b>a) return 0;
    b=(jc[a-b]*jc[b])%MOD;
    a=jc[a];
    int c=gcd(a,b);
    a/=c;
    b/=c;
    Extended_gcd(b,MOD);
    x=(x+MOD)%MOD;
    x=(x*a)%MOD;
    return x;
}
int Combination(int n, int m){
    int ans=1;
    int a,b;
    while(m||n){
        a=n%MOD;
        b=m%MOD;
        n/=MOD;
        m/=MOD;
        ans=(ans*C(a,b))%MOD;
    }
    return ans;
}
int init(){
    jc[0]=1;
    for(int i=1;i<=MOD;i++) jc[i]=(jc[i-1]*i)%MOD;
}
int main(){
    int m,n;
    while(~scanf("%d%d",&n,&m)){
        printf("%d\n",Combination(n,m));
    }
    return 0;
}