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;
const int maxn = 50 + 5;
const int maxm = 2500 + 10;
int a[maxn];
ll f[maxm << 1];
int main()
{
	int n, x;
	scanf("%d%d", &n, &x);
	for(int i = 1; i <= n; ++i)
	{
		scanf("%d", &a[i]);
		a[i] -= x;
	}
	f[maxm] = 1;
	for(int i = 1; i <= n; ++i)
		if(a[i] >= 0)
		{
			for(int j = (maxm << 1) - 1; j >= a[i]; --j)
				f[j] += f[j - a[i]];
		}
		else
		{
			for(int j = 0; j < (maxm << 1) + a[i]; ++j)
				f[j] += f[j - a[i]];
		}
	cout << f[maxm] - 1 << endl;
	return 0;
}