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;

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 = 1; i <= N; i++) {
			x[i] = sc.nextInt();
		}
		long[][][] dp = new long[N + 1][N + 1][N * A + 1];
		
		for(int i = 0; i <= N; i++) {
			for(int j = 0; j <= N; j++) {
				for(int k = 0; k <= N * A; k++) {
					if(i == 0 && j == 0 && k == 0) {
						dp[i][j][k] = 1;
					} else if(i > 0 && x[i] > k) {
						dp[i][j][k] = dp[i - 1][j][k];
					} else if(i > 0 && j > 0 && x[i] <= k) {
						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 += dp[N][i][i * A];
		}
		System.out.println(ans);
	}
	
}