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 {
	private static Scanner sc = new Scanner(System.in);
	public static void main(String[] args) {
		int n = sc.nextInt();
		int a = sc.nextInt();
		int[] d = new int[51];
		for (int i = 0;i < n;i++) d[i] = sc.nextInt();
		long[][][] dp = new long[60][60][2510];
		dp[0][0][0] = 1;
		for (int i = 0;i < n;i++) {
			int x = d[i];
			for (int j = 0;j < n;j++) {
				for (int k = 0;k < 2500;k++) {
					if (dp[i][j][k]>0) {
						dp[i+1][j][k] += dp[i][j][k];
						dp[i+1][j+1][k+x] += dp[i][j][k];
					}
				}
			}
		}

		long ret = 0;

		for (int i = 1;i <= n;i++) {
			for (int j = 1;j <= 2500;j++) {
				if (i*a==j&&dp[n][i][j]>0) {
					ret += dp[n][i][j];
				}
			}
		}

		System.out.println(ret);
	}
}