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.Arrays;
import java.util.Scanner;

public class Main {
  Scanner sc = new Scanner(System.in);

  public static void main(String[] args) {
    new Main().run();
  }

  void run() {
    int n = ni();
    int a = ni();
    int[] x = new int[n];
    for (int i = 0; i < n; ++i) {
      x[i] = ni();
    }
    long[][] dp = new long[n + 1][2501];
    dp[0][0] = 1;
    for (int i = 0; i < n; ++i) {
      for (int j = 0; j <= 2500; ++j) {
        for (int k = n; 0 <= k; --k) {
          int nk = k + 1;
          int nv = j + x[i];
          dp[nk][nv] += dp[k][j];
        }
      }
    }

    long cnt = 0;
    for (int i = 1; i <= n; ++i) {
      for (int j = 1; j <= 2500; ++j) {
        if (j / i == a && j % i == 0) {
          cnt += dp[i][j];
        }
      }
    }
    System.out.println(cnt);
  }

  int ni() {
    return Integer.parseInt(sc.next());
  }

  void debug(Object... os) {
    System.err.println(Arrays.deepToString(os));
  }
}