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);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int l = m * n;
		int[] a = new int[n];
		for(int i=0;i<n;i++) {
			a[i] = sc.nextInt();
		}
		long[][][] dp = new long[n+1][n+1][l+1];
		dp[0][0][0] = 1;
		for(int i=0;i<n;i++) {
			for(int j=0;j<=n;j++) {
				for(int k=0;k<=l;k++) {
					dp[i+1][j][k] += dp[i][j][k];
					if (j < n && k + a[i] <= l) {
						dp[i+1][j+1][k+a[i]] += dp[i][j][k];
					}
				}
			}
		}
		long ans = 0;
		for(int i=1;i<=n;i++) {
			ans += dp[n][i][i*m];
		}
//		System.out.println(Arrays.deepToString(dp));
		System.out.println(ans);
	}

}
