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>
#include<cstring>
using namespace std;
#define ll long long
ll dp[2500][50];
ll a[50];
; int main()
{
	int n, ave;
	cin >> n >> ave;
	for (int i = 0; i < n; i++)
		cin >> a[i];
	memset(dp, 0, sizeof(dp));
	dp[0][0] = 1;
	for (int i = 0; i < n; i++)
		for (int j = n * 50; j >= a[i]; j--)
			for (int k = 1; k <= n; k++)
				if (dp[j - a[i]][k - 1])
					dp[j][k] += dp[j - a[i]][k - 1];
	ll ans = 0;
	for (int i = 1; i <= n; i++)
		ans += dp[i * ave][i];
	cout << ans << endl;
	return 0;
}