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

public class Main {
  static int n, a;
  static int[] x;

  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);

    n = sc.nextInt(); a = sc.nextInt();
    x = new int[n];
    for(int i = 0; i < n; i++){
      x[i] = sc.nextInt();
    }

    long[][][] dp = new long[n + 1][n + 1][n * 50 + 1];
    dp[0][0][0] = 1;
    for(int i = 1; i <= n; i++){
      for(int j = 0; j <= n; j++){
        for(int k = 0; k < dp[i][j].length; k++){
          if(j - 1 >= 0 && k - x[i - 1] >= 0){
            dp[i][j][k] += dp[i - 1][j - 1][k - x[i - 1]];
          }
          dp[i][j][k] += dp[i - 1][j][k];
        }
      }
    }

    long count = 0;
    for(int i = 1; i <= n; i++){
      int tar = i * a;
      count += dp[n][i][tar];
    }

    System.out.println(count);
  }
}