Mathematical knowledge: finding combinatorial number I - finding combinatorial number

subject ：AcWing 885. Find the combination number I
Given n Group inquiry , Each group is given two integers a,b, Please output Cbamod(10⁹+7) Value .

Input format
The first line contains integers n.

Next n That's ok , Each line contains a set of a and b.

Output format
common n That's ok , Each line outputs a solution to the query .

Data range
1≤n≤10000,
1≤b≤a≤2000

sample input ：

3
3 1
5 3
2 2

sample output ：

3
10
1

Topic analysis ：
According to the principle of addition and counting, there are ：
C^b_a=C^b−1_a−1+C^b_a−1
So you can preprocess first , Then directly look up the table

#include <iostream>

using namespace std;

const int N = 2010 ,mod = 1e9+7;
int c[N][N];

void init() //  The value of the number of preprocessing combinations 
{
    
    for(int i=0;i<N;i++) //  Can't be equal  N  Superboundary 
        for(int j=0;j<=i;j++)
            if(!j)c[i][j]=1;
            else c[i][j]=(c[i-1][j-1]+c[i-1][j])%mod;
}
int main()
{
    
    init();
    int n;
    cin>>n;
    while(n--)
    {
    
        int a,b;
        cin>>a>>b;
        cout<<c[a][b]<<endl;
    }
    return 0;
}