第一种：
1<=n,m<=1000,mod<=1e9,用杨辉三角做
例题

#include<stdio.h>
#include <string.h>
#include<cmath>
#include<algorithm>
using namespace std;
const int N=1001;
long long  Triangle[N][N];
void creat()
{
    Triangle[0][0]=1;
    for(int i=1;i<N;i++)
    {
        Triangle[i][0]=1;
        for(int j=1;j<i;j++)
        {
            Triangle[i][j]=Triangle[i-1][j-1]+Triangle[i-1][j];
        }
        Triangle[i][i]=1;
    }

}
int main()
{
    int c;
    int a,b;
    creat();
    while(~scanf("%d",&c))
    {
        while(c--)
        {
            scanf("%d%d",&a,&b);
            printf("%d\n",(int)(Triangle[a][b]));
        }
    }
}
/***************************************************
User name: Gitfan
Result: Accepted
Take time: 0ms
Take Memory: 7000KB
Submit time: 2017-02-23 12:19:22
****************************************************/