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;

int n, a, x[50];
long long dp[51][2501] = { 1 }, ans = 0;

int main() {
	cin >> n >> a;
	for (int i = 0; i < n; i++)
		cin >> x[i];
	for (int i = 0; i < n; i++)
		for (int j = i; j >= 0; j--)
			for (int k = 0; k <= 50 * i; k++)
				dp[j + 1][k + x[i]] += dp[j][k];
	for (int i = 1; i <= n; i++)
		ans += dp[i][a * i];

	cout << ans << endl;
}
