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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
	int n;
	int[] x;
	long[][][] dp;

	long dp(int k, int t, int s) {
		if (k < 0 || t < 0 || s < 0) {
			return 0;
		}
		if (k == 0) {
			if (t == 0 && s == 0) {
				return 1;
			}
			if (t == 1 && s == x[0]) {
				return 1;
			}
			return 0;
		}
		if (0 <= dp[k][t][s]) {
			return dp[k][t][s];
		}

		long ret = dp(k - 1, t, s);
		ret += dp(k - 1, t - 1, s - x[k]);
		return dp[k][t][s] = ret;
	}

	void run() {
		Scanner sc = new Scanner(System.in);

		n = sc.nextInt();
		int a = sc.nextInt();
		x = new int[n];
		for (int i = 0; i < n; i++) {
			x[i] = sc.nextInt();
		}
		long ans = 0;
		dp = new long[n][n + 1][a * n + 1];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n + 1; j++) {
				Arrays.fill(dp[i][j], -1);
			}
		}
		for (int i = 1; i <= n; i++) {
			ans += dp(n - 1, i, a * i);
		}
		System.out.println(ans);
	}

	public static void main(String[] args) {
		new Main().run();
	}
}