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;
int n,a,x[100],cnt;ll dp[51][51][3000],ans;
ll dfs(int pos,int las,int sum)
{
	if(pos>n)
	{
		if(las==0&&sum==cnt*a)return 1;
		else return 0;
	}
	if(dp[pos][las][sum]!=-1)return dp[pos][las][sum];
	return dp[pos][las][sum]=dfs(pos+1,las-1,sum+x[pos])+dfs(pos+1,las,sum);
}
int main()
{
	ios::sync_with_stdio(0);
	cin>>n>>a;
	for(int i=1;i<=n;i++)
		cin>>x[i];
	for(int i=1;i<=n;i++)
		cnt=i,memset(dp,-1,sizeof dp),ans+=dfs(1,i,0);
	cout<<ans<<endl;	
}