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;
int main(){
  ll n,a;
  cin>>n>>a;
  ll x[n];
  ll i,j,k;
  for(i=0;i<n;i++) cin>>x[i];
  ll dp[2][n+1][50*50+100];
  memset(dp,0,sizeof(dp));
  dp[0][0][0]=1;
  for(i=0;i<n;i++){
    for(j=0;j<50*50+50;j++){
      for(k=0;k<n;k++){
	dp[(i+1)%2][k+1][j+x[i]]+=dp[i%2][k][j];
	dp[(i+1)%2][k][j]       +=dp[i%2][k][j];
	dp[i%2][k][j]=0;
      }
    }
  }
  ll ans=0;
  for(i=1;i<=n;i++) ans+=dp[n%2][i][i*a];
  cout << ans << endl;
  return 0;
}
