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;

long memo[51][51][2501];
int N, A, x[51];

long func(int i, int num, int sum)
{
    if (i<0 || num<0 || sum<0) return 0;
    if (num==0 && sum==0) return 1;
    auto& res=memo[i][num][sum];
    if (~res) return res;
    return res=func(i-1, num-1, sum-x[i-1])+func(i-1, num, sum);
}

int main()
{
    memset(memo, -1, sizeof(memo));
    cin>>N>>A;
    for(int i=0; i<N; ++i) cin>>x[i];

    long res=0;
    for(int i=1; i<=N; ++i) res+=func(N, i, i*A);
    cout<<res<<endl;
}