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: Runtime Error)

import java.util.Scanner;

/**
 *
 * @author Colors
 */
public class Main {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int a = sc.nextInt();
        int x[] = new int[n];
        long ans = 0L;
        for (int i = 0; i < n; i++) {
            x[i] = sc.nextInt();
        }
        for (int i = 0; i < n; i++) {
            int chooseCard[] = new int[i + 1];
            for (int j = 0; j < chooseCard.length; j++) {
                chooseCard[j] = j;
            }
            int ave = 0;
            for (int j = 0; j < chooseCard.length; j++) {
                ave += x[chooseCard[j]];
            }
            ave /= chooseCard.length;
            if (ave == a) {
                ans++;
            }
            for (int j = 1; j < chooseCard.length; j++) {
                if (chooseCard[chooseCard.length] == n) {
                    if (chooseCard[chooseCard.length - j] + 1 < chooseCard[chooseCard.length - j - 1]) {
                        chooseCard[chooseCard.length - j]++;
                    }
                }
            }
        }
        System.out.println(ans);
    }

}