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 ll;

ll mem[55][55*55][55];
int a[55] , n , A ;


ll dp(int i,int sum,int cnt){
if( i==n ){
    return ( sum==A*cnt && cnt>0 )?1ll:0ll;
}

ll &ret=mem[i][sum][cnt];
if( ret !=-1 )return ret;

return ret=dp(i+1,sum,cnt)+dp(i+1,sum+a[i],cnt+1);
}

int main(){
scanf("%d %d",&n,&A);
for(int i=0;i<n;i++)scanf("%d",a+i);
memset(mem,-1,sizeof mem);
printf("%lld\n",dp(0,0,0));
return 0;
}
