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;

const int MAXN = 55;
long long dp[MAXN][MAXN * MAXN];
int n, A, a[MAXN];

int main() {
	cin >> n >> A;
	for (int i = 0; i < n; i++)
		cin >> a[i];
	dp[0][0] = 1;
	for (int t = 0; t < n; t++)
		for (int j = MAXN * MAXN - 1; j >= 0; j--)
			for (int i = MAXN - 1; i >= 1; i--)
				if (j - a[t] >= 0)
					dp[i][j] += dp[i - 1][j - a[t]];
	long long ans = 0;
	for (int i = 1; i <= n; i++)
		ans += dp[i][i * A];
	cout << ans;
}