Count no of subsets with given sum

//count the number of subsets with given sum
// correct only if each values[i] is greater than 0
int solve(vector<int> value , int target){
    int  n = value.size();
    int sum=0;
    for(int a=0;a<n;a++)sum+=value[a];
    if(target > sum) return 0;
    vector<vector<int>> dp (n+1 ,vector<int>(sum+1,0));
    // a represents the ath element .. b represents the knapsack present

    for(int a=0;a<=n;a++)dp[a][0] = 1;// sum 0 is possible even if do not select anything

    for(int a=1;a<=n;a++){
        for(int b=1;b<=sum;b++){
            if(value[a-1]<=b){
            dp[a][b] = dp[a-1][b-value[a-1]] + dp[a-1][b]; //either i choose the ath element or not
            }else{
            dp[a][b] = dp[a-1][b]; // cant choose the ath element becuase its weight is more
            }
        }
    }
    return dp[n][target];

}