Coin Change-no of ways to get a total

given some coins with infinite supply . we have to find the number of ways to get a given total(sum).

example
n=3
coins={1,2,3}
sum=5

output => 5 (total ways)

1 1 1 1 1    --- 1st
1 1 1 2    --- 2nd
1 1 3    --- 3rd
2 3    --- 4th
1 1 2    --- 5th


we will use dynamic programming to solve this question:
y is no. of test cases
n is no of different coins
a[] array to store coins
c++ implementation:

#include <iostream>
using namespace std;


void coins(int a[],int n,int sum)
{    
      int t[n+1][sum+1];     
   
   for(int i=0;i<=n;i++)      
      t[i][0]=1;
      
   for(int j=1;j<=sum;j++)
      t[0][j]=0;
      
    
       for(int i=1;i<=n;i++)
       {
           for(int j=1;j<=sum;j++)
           {
              if(a[i-1]>j)  
              t[i][j]=t[i-1][j];
            else
            t[i][j]=t[i][j-a[i-1]]+t[i-1][j];
             
           }
       }
       
    
      cout<< t[n][sum];
}



int main() {
int y; cin>>y;
while(y--)
{  int n;  
   cin>>n;
   
int a[n];
for(int i=0;i<n;i++)
cin>>a[i];

int sum;   
cin>>sum;

coins(a,n,sum);
  cout<<endl;  
}
 return 0;
}