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: Wrong Answer)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
    static final int R = 2500;

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt(), a = in.nextInt();
        int[] v = new int[n];
        for (int i = 0; i < n; ++i) v[i] = in.nextInt();

        long[][] dp = new long[n + 1][R + 1];
        dp[0][0] = 1;

        for (int i = 0; i < n; ++i) {
            for (int j = R; j >= 0; --j) {
                for (int k = n; k >= 0; --k) {
                    if (dp[k][j] == 0) continue;
                    dp[k + 1][j + v[i]] += dp[k][j];
                }
            }
        }
        int res = 0;
        for (int i = 1; i <= n; ++i) {
            for (int j = 1; j <= R; ++j) {
                if (j / i == a && j % i == 0) {
                    res += dp[i][j];
                }
            }
        }
        System.out.println(res);
    }
}