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 int ll;
#define FOR(i,l,r) for(i=l;i<r;i++)
#define REP(i,n) FOR(i,0,n)
#define ALL(x) x.begin(),x.end()
#define P pair<ll,ll>
#define F first
#define S second
signed main(){
  ll N,A,i,j,k;cin>>N>>A;ll X[N],DP[N+1][4901];
  REP(i,N){cin>>X[i];X[i]-=A;}
  REP(i,4901)DP[0][i]=0;DP[0][2450]=1;
  FOR(i,1,N+1)REP(j,4901){
    DP[i][j]=DP[i-1][j];
    if(j-X[i-1]>=0&&j-X[i-1]<=4900)DP[i][j]+=DP[i-1][j-X[i-1]];
  }
  cout<<DP[N][2450]-1<<endl;
  return 0;
}