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 dfs(int cnt,int sum);
int n,x[100];
long long memo[59][50009];

int main(){
  int a;
  memset(memo,-1,sizeof(memo));
  cin>>n>>a;
  for(int i=0;i<n;i++){
    cin>>x[i];
    x[i]-=a;
  }
  cout<<dfs(0,2500)-1<<endl;
  return(0);
}

long long dfs(int cnt,int sum){
  long long rec=0;
  if(memo[cnt][sum]!=-1)return memo[cnt][sum];
  if(cnt==n){
    if(sum==2500)return 1;
    else return 0;
  }
  rec+=dfs(cnt+1,sum);
  rec+=dfs(cnt+1,sum+x[cnt]);
  return memo[cnt][sum]=rec;
}
