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
/*
* @Author Silviase(@silviasetitech)
* For ProCon
*/

import java.util.*;
import java.lang.*;
import java.math.*;

class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        
        int n = sc.nextInt();
        int a = sc.nextInt();
        int[] num = new int[n+1];
        long ans = 0;
        long[][][] dp = new long[n+1][n+1][n*a+1];


        num[0] = 1000000007;
        for (int i = 1; i <= n; i++) {
            num[i] = sc.nextInt();
        }

        for (int i = 0; i <= n; i++) {
            for (int j = 0; j <= i; j++) {
                for (int k = 0; k <= n*a; k++) {
                    if (i == 0 && j == 0 && k == 0) {
                        dp[i][j][k] = 1;
                    }else if(i >= 1 && k < num[i]){
                        dp[i][j][k] = dp[i-1][j][k];
                    }else if(i >= 1 && j >= 1 && k >= num[i]){
                        dp[i][j][k] = dp[i-1][j][k] + dp[i-1][j-1][k-num[i]];
                    }else{
                        dp[i][j][k] = 0;
                    }
                }
            }
        }

        for (int i = 1; i <= n; i++) {
            ans += dp[n][i][i*a];
        }
        System.out.println(ans);

        sc.close();
    }

}