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>
#define ll long long
using namespace std;
const int N=2500;
ll dp[55][5005];
int n,m,x,y;
int main()
{
	cin>>n>>m;
	dp[0][2500]=1;
	for(int i=1;i<=n;i++)
	{
		cin>>x;
		y=x-m;
		for(int j=0;j<=5000;j++)
		{
			dp[i][j]+=dp[i-1][j];
			if(j+y<0||j+y>5000)continue;
			dp[i][j+y]+=dp[i-1][j];
		}
	}
	cout<<dp[n][2500]-1<<endl;
	return 0;
}