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 <iostream>
#include<math.h>
#include<string.h>
#include<algorithm>
typedef long long int ll;
using namespace std;
int main(){
    ll n,a,s,x,i,j;
    cin>>n>>a;
    ll k[n],sum[10000][n+1];
    memset(sum,10000*n*sizeof(int),0);
    for(i=0;i<n;i++){
        cin>>s;
        k[i]=s-a;
    }

    sum[5000][0]=1;
    for(i=0;i<n;i++){
        for(j=0;j<10000;j++){
            if(0<=j-k[i]&&j-k[i]<10000)x=sum[j-k[i]][i];
            else x=0;
            sum[j][i+1]=sum[j][i]+x;
        }
    }

    cout<<sum[5000][n]-1<<endl;

}