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();
		int A=sc.nextInt();
		int[] x=new int[N+1];
		for(int i=0;i<N;i++)x[i+1]=sc.nextInt();
		long count=0;
		//dp[i][j][k]:i枚目まででj枚使って合計kを作る
		int[][][]dp=new int[N+1][N+1][2501];
		
		for(int i=0;i<=N;i++){
			for(int j=0;j<=i;j++){
				for(int k=0;k<2501;k++){
					if(i==0 && j==0 && k==0)dp[i][j][k]=1;
					else if(i>=1 &&x[i]>k)dp[i][j][k]=dp[i-1][j][k];
					else if(i>=1 && j>=1 && x[i]<=k)dp[i][j][k]=dp[i-1][j][k]+dp[i-1][j-1][k-x[i]];
				}
			}
		}
		for(int j=1;j<=N;j++){
				count+=dp[N][j][j*A];
		}
		
		System.out.println(count);
	}
}