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 <iostream>
using namespace std;
int x[55];
long long dp[55][55*55];
int main()
{
	int n,a;
	cin >> n >> a;
	dp[0][0] = 1;
	for(int i = 1;i <= n;i++)
	cin >> x[i];
	for(int i = 1;i <= n;i++)
	{
		for(int j = i-1;j >= 0;j--)
		for(long long k = 55*j;k >=0 ;k--)
		dp[j+1][k+x[i]] += dp[j][k];
	}
	long long ans = 0;
	for(int i = 1;i <= n;i++)
	{
		ans += dp[i][i*a];
	}
	cout << ans << endl;
	return 0;
}