Problem:
Score : 300 points

Problem Statement

Tak has N cards. On the i-th (1 \leq i \leq N) card is written an integer x_i.
He is selecting one or more cards from these N cards, so that the average of the integers written on the selected cards is exactly A.
In how many ways can he make his selection?

Constraints

1 \leq N \leq 50

1 \leq A \leq 50

1 \leq x_i \leq 50

N,\,A,\,x_i are integers.

Partial Score

200 points will be awarded for passing the test set satisfying 1 \leq N \leq 16.

Input

The input is given from Standard Input in the following format:

N A
x_1 x_2 ... x_N

Output

Print the number of ways to select cards such that the average of the written integers is exactly A.

Sample Input 1

4 8
7 9 8 9

Sample Output 1

5

The following are the 5 ways to select cards such that the average is 8:

Select the 3-rd card.

Select the 1-st and 2-nd cards.

Select the 1-st and 4-th cards.

Select the 1-st, 2-nd and 3-rd cards.

Select the 1-st, 3-rd and 4-th cards.

Sample Input 2

3 8
6 6 9

Sample Output 2

0

Sample Input 3

8 5
3 6 2 8 7 6 5 9

Sample Output 3

19

Sample Input 4

33 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Sample Output 4

8589934591

The answer may not fit into a 32-bit integer.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)



import java.math.BigDecimal;
        import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int a = sc.nextInt();
        int[] x = new int[n];
        for (int i = 0; i < n; i++) {
            x[i] = sc.nextInt();
        }
        
        long[][][] dp = new long[n+1][n+1][a*n+1];
        
        dp[0][0][0] = 1;

        for (int i = 0; i < n; i++) {
            for (int k = 0; k < n; k++) {
                for (int j = 0; j <= a*n; j++) {
                    dp[i + 1][k][j] += dp[i][k][j];
                    if (j >= x[i]) dp[i + 1][k + 1][j] += dp[i][k][j - x[i]];
                }
            }

        }

        long ans = 0;
        for (int k = 1; k <= n; k++) {
            ans += dp[n][k][k * a];
        }
        System.out.println(ans);

    }

}