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 <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <string>
using namespace std;
typedef long long ll;
int n,a;
int x[55];

ll dp[55][55][55*55];
ll solve(int k,int c,int s){
  if(k == n){
    return (c*a==s?1:0);
  }
  if(dp[k][c][s] >= 0) return dp[k][c][s];
  return dp[k][c][s] = solve(k+1,c+1,s+x[k]) + solve(k+1,c,s);
}

int main(void){
  cin >> n >> a;
  for(int i = 0; i < n; i++){
    cin >> x[i];
  }
  memset(dp,-1,sizeof(dp));
  cout << solve(0,0,0)-1 << endl;
}
