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
#include<bits/stdc++.h>
using namespace std;
long long dp[55][55][55*55];
int x[55];
int main()
{
	int n,a;
	cin>>n>>a;
	for(int i=1;i<=n;i++)
		cin>>x[i];
	dp[1][1][x[1]]=1;
	for(int i=2;i<=n;i++)
		for(int j=1;j<=n;j++)
			for(int k=1;k<=a*n;k++)
			{
				dp[i][j][k]=dp[i-1][j][k]+dp[i-1][j-1][k-x[i]];
				if(j==1)
					dp[i][j][k]+=(x[i]==k);
			}
	long long sum=0;
	for(int i=1;i<=n;i++)
		sum+=dp[n][i][a*i];
	cout<<sum<<endl;
	return 0;
}
