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 <iostream>
typedef long long LL;
using namespace std;
LL dp[55][2501];
int now;
int main(){
    dp[0][0]=1;
    int n,m,k,t;
    int a;
    LL ans=0;
    cin>>n>>a;
    for (int i=1; i<=n; ++i) {
        scanf("%d",&k);
        now+=k;
        for (int j=i; j>=1; --j) {
            for (t=now; t>=k; --t) {
                dp[j][t]+=dp[j-1][t-k];
            }

        }
    }
    for (int i=1; i<=n; ++i)ans+=dp[i][a*i];
    printf("%lld\n",ans);
}
