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.

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.

Examples

Input

4 8
7 9 8 9


Output

5


Input

3 8
6 6 9


Output

0


Input

8 5
3 6 2 8 7 6 5 9


Output

19


Input

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


Output

8589934591
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		StringBuilder sb = new StringBuilder();
		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][50 * n + 1];
		dp[0][0][0] = 1;
		for (int i = 1; i <= n; i++) {
			for (int j = 0; j <= n; j++) {
				for (int k = 0; k <= 50 * n; k++) {
					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 += dp[n][i][i * a];
		}
		System.out.println(ans);
	}
}