Given n distinct positive integers, integer k (k <= n) and a number target.

Find k numbers where sum is target. Calculate how many solutions there are?

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Example
Given [1,2,3,4], k = 2, target = 5.

There are 2 solutions: [1,4] and [2,3].

Return 2.

public int kSum(int A[], int k, int target) {
        // write your code here
        //state 
        int n = A.length;
        int[][][] f = new int[n + 1][k + 1][target + 1];
        
        //initialize
        for (int i = 0; i <= n; i++) {
            f[i][0][0] = 1;
        }
        
         //function
        for (int i = 1; i <= n; i++) {
             for (int j = 1; j <= k && j <= i; j++) {
                 for (int l = 1; l <= target; l++) {
                     
                    f[i][j][l] = f[i - 1][j][l];
                    if (l >= A[i - 1]) {
                        f[i][j][l] += f[i - 1][j - 1][l - A[i - 1]];
                    }
                }
            }
        }
        
        return f[n][k][target];
    }