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;

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

    int N = scanner.nextInt();
    int A = scanner.nextInt();

    int[] x = new int[N + 1];
    for (int i = 1; i <= N; i++) x[i] = scanner.nextInt();

    long[][][] dp = new long[N + 1][N + 1][2501];
    for (int i = 0; i <= N; i++) dp[i][0][0] = 1;
    for (int i = 1; i <= N; i++) {
      for (int j = 1; j <= i; j++) {
        for (int k = 1; k <= 2500; k++) {
          dp[i][j][k] = dp[i - 1][j][k];
          if (k >= x[i]) dp[i][j][k] += dp[i - 1][j - 1][k - x[i]];
        }
      }
    }

    long count = 0;
    for (int j = 1; j <= N; j++) count += dp[N][j][A * j];
    System.out.println(count);
  }
}