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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
	public static void main(String[] args) throws NumberFormatException, IOException{
		BufferedReader rd = new BufferedReader(new InputStreamReader(System.in), 1);
		String str = rd.readLine();
	    String[] sl = str.split(" ");
	    int n = Integer.parseInt(sl[0]);
	    int a = Integer.parseInt(sl[1]);
	    str = rd.readLine();
	    sl = str.split(" ");
	    int x[] = new int[51];
	    long v[][][] = new long[51][51][2501];
	    for(int i = 1; i <= n; i++)
		{
			x[i] = Integer.parseInt(sl[i - 1]);
		}
	    
	    v[1][1][x[1]] = 1;
	    v[1][0][0] = 1;
	    for(int i = 2; i <= n; i++)
	    {
	    	for(int j = 0; j <= i; j++)
	    	{
	    		for(int k = 0; k <= 50 * i; k++)
	    		{
	    			v[i][j][k] += v[i - 1][j][k];
	    		}
	    	}
	    	for(int j = 1; j <= i; j++)
	    	{
	    		for(int k = x[i]; k <= 50 * i; k++)
	    		{
	    			v[i][j][k] += v[i - 1][j - 1][k - x[i]];
	    		}
	    	}
	    }
	    
	    long ans = 0;
	    for(int i = 1; i <= n; i++)
	    {
	    	for(int j = 1; j <= n; j++)
	    	{
	    		ans += v[i][j][a * j] - v[i - 1][j][a * j];
	    	}
	    }
	    
		System.out.println(ans);
		
  	}
}