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;
typedef long long ll;
ll dp[51][5000];

int main(){
  int n,A,a[51];
  cin>>n>>A;
  for(int i=0;i<n;i++) cin>>a[i];

  
  dp[0][0]=1;
  for(int i=0;i<n;i++)
    for(int k=3000;k>=0;k--)
	for(int j=0;j<n;j++)
	dp[j+1][k+a[i]]+=dp[j][k];

  ll ans=0;
  for(int j=1;j<=n;j++)
    for(int k=1;k<=3000;k++)if(1.0*k/j==A)ans+=dp[j][k];
    cout <<ans<<endl;
    return 0;
  }
