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.Scanner;

public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt(), A = sc.nextInt();
		int[] x = new int[N];
		for(int i = 0; i < N; i++) x[i] = sc.nextInt();
		int[][][] dp = new int[N + 1][N + 1][2501];
		dp[0][0][0] = 1;
		for(int i = 0; i < N; i++) {
			for(int j = 0; j < N + 1; j++) {
				for(int k = 0; k < 2501; k++) {
					if(j + 1 < N + 1 && k + x[i] < 2501) dp[i + 1][j + 1][k + x[i]] += dp[i][j][k];
					dp[i + 1][j][k] += dp[i][j][k];
				}
			}
		}
		long ans = 0;
		for(int k = 1; k <= N; k++) {
			ans += (long)dp[N][k][A * k];
		}
		System.out.println(ans);
	}
}