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 pb push_back
#define mp make_pair
#define int long long
#define inf 1000000007
#define LINF 100000000000000007LL
#define ll long long
using namespace std;
map<int,int> mope[51];
signed main(){
	int n,a;
	cin>>n>>a;
	vector<int> x(n);
	for(int i=0;i<n;i++){
		cin>>x[i];
		x[i] -= a;
	}
	mope[0][0] = 1;
	for(int i=1;i<=n;i++){
		int cur = x[i-1];
		for(int j = -3000; j<=3000; j++){
			mope[i][j+cur] += mope[i-1][j];
			mope[i][j] += mope[i-1][j];
		}
	}
	cout<<mope[n][0]-1<<endl;
	return 0;
}