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.*;

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