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.Arrays;
import java.util.Scanner;

class Main{



	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);			//文字の入力
		int n = sc.nextInt();
		int a = sc.nextInt();
		int[] x = new int[n+1];
		for(int i = 1;i <= n;i++){
			x[i] = sc.nextInt();
		}
		Arrays.sort(x);

		long[][][] dp = new long[51][51][50*50+1];

		
		for(int i = 0;i <= n;i++){
			for(int j = 0;j<= n;j++){
				for(int k = 0;k <= 2500;k++){
					if(i == 0 && j == 0 && k == 0){
						dp[i][j][k] = 1;
						
						
					}else if(i >= 1 && k < x[i]){
						
						dp[i][j][k] = dp[i-1][j][k];
					}else if(i >= 1 && j >= 1 && k >= x[i]){
						
						dp[i][j][k] = dp[i-1][j][k] + dp[i-1][j-1][k-x[i]];
					}else{
						
						dp[i][j][k] = 0;
					}
				}
			}
		}
		
		long ans = 0;
		for(int i = 1;i <= n;i++){
			ans += (long)dp[n][i][i*a];
		}

		System.out.println(ans);

	}
}