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[] x = new int[N];
		for(int i=0; i<N; i++)
			x[i] = sc.nextInt();
		
		long[][] dp = new long[N+1][50*N+1];
		dp[0][0] = 1;
		for(int i=0; i<N; i++)
			for(int j=i; j>=0; j--)
				for(int k=0; k<=50*i; k++)
					dp[j+1][k+x[i]] += dp[j][k];
		
		long ans = 0;
		for(int i=1; i<=N; i++)
			ans += dp[i][i*A];
		System.out.println(ans);
		sc.close();
	}
}
