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: Time Limit Exceeded)

import java.util.Scanner;

public class Main {
	
	public static long recursAvg(int[] ar, int start, int sum) {
		if(ar.length==start){
			if(sum==0){
				return 1;
			}
			return 0;
		}
		return recursAvg(ar, start+1, sum+ar[start]) + recursAvg(ar, start+1, sum);
		//return 0;
	}


	
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		
		String[] info = scanner.nextLine().split(" ");
		int avg = Integer.parseInt(info[1]);
		String[] str = scanner.nextLine().split(" ");
		int[] stuff = new int[str.length];
		for(int x = 0; x<stuff.length; x++){
			stuff[x] = Integer.parseInt(str[x]) - avg;
		}
		

		System.out.println(recursAvg(stuff, 0, 0)-1);
		
	}

}