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 sc = new Scanner(System.in);
		int n = sc.nextInt();
		int q = sc.nextInt();
		int[] a = new int[n];
		int sum= 0;
		for(int i =0; i<n; i++){
			a[i]=sc.nextInt();
			sum+=a[i];
		}
		long[][][] dp=new long[n+1][n+1][sum+1];
		
		for(int i = 0; i<n+1; i++){
			for(int j = 0; j<n+1; j++){
				for(int k = 0; k<sum+1; k++){
					
					if(i>=1 && k<a[i-1]){
						dp[i][j][k]=dp[i-1][j][k];
					}else if(j>=1 && i>=1 && k>=a[i-1]){
						dp[i][j][k]=dp[i-1][j][k]+dp[i-1][j-1][k-a[i-1]];
					}else{
						dp[i][j][k]=0;
					}
					if(i==0 && j==0 && k==0){
						dp[0][0][0]=1;
					}
				}
			}
		}
		long ans=0;
		for(int i = 1; i<n+1; i++){
			if(i*q<=sum){
				ans+=dp[n][i][i*q];
			}
		}
		System.out.println(ans);
	}
}