Number of ways N dices can make sum S

Problem: Given N dices. Each dice has A faces.
Find the total number of ways these dices can make sum S when all are thrown together.
// the below code is written in C++.
#include<bits/stdc++.h>
using namespace std;
int main()
{
int s=10;  // This is the required Sum we want to generate
int n=5;   // n is total number of dices.
int A=6;
// A is number of faces each dice has. Each face has one unique number from 1 to A.
int i,j,k;

// d[i][j] depicts number of ways i dices can make sum of j.
long long int d[n+1][s+1];

// setting no. of ways for one dice to make sum 1 to A as 1.
for(i=1;i<=A;i++)
{
d[1][i]=1;
}

// after A, no. of ways is 0.
for(i=A+1;i<=s;i++)
{
d[1][i]=0;
}

// setting no. of ways for all dices to make sum 0 as 0.
for(i=1;i<=n;i++)
d[i][0]=0;

for(i=2;i<=n;i++)    // for i no. of dices.
{
   for(j=1;j<=s;j++) //  for sum j.
   {
        long long int cnt=0;
        for(k=1;k<=A;k++)     // for each face.
        {
            if(j-k>=0)
            {
//  taking k for i-th dice and taking rest j-k for other (i-1) dices.
               cnt+=d[i-1][j-k];      
            }
        }
        d[i][j]=cnt;
   }
}
cout<<"no. of ways : "<<d[n][s]<<endl;

return 0;
}

Complexities :

Time complexity:    O(N*S*A)

Space complexity:   O(N*S)