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>
#define mp make_pair
#define pb push_back
#define pii pair<int,int>
#define LL long long
#define st first
#define nd second
using namespace std;
LL dp[2501][51];
int main(){
    LL n,a,t,ans=0;
    cin>>n>>a;
    dp[0][0]=1;
    for(int i=0;i<n;++i){
        cin>>t;
        for(int j=2500;j>=t;--j)
            for(int o=0;o<=i;++o)
                dp[j][o+1]+=dp[j-t][o];
    }
    for(int i=1;i<=2500;++i){
        if(i%a!=0||i/a>n)
            continue;
        ans+=dp[i][i/a];
    }
    cout<<ans<<endl;
}

