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;

const int N = 55;
const int offset = N * N;

int n, A, a[N];
long long f[N][offset + offset];

int main() {
	ios_base::sync_with_stdio(false); cin.tie(0);
	cin >> n >> A;
	for (int i = 1; i <= n; ++i) cin >> a[i], a[i] -= A;

	f[0][offset] = 1;
	for (int i = 1; i <= n; ++i) {
		for (int j = 0; j < offset + offset; ++j) {
			f[i][j] = f[i-1][j];
			if (j - a[i] >= 0 && j - a[i] < offset + offset) {
				f[i][j] += f[i-1][j - a[i]];
			} 
		}
	}

	cout << f[n][offset] - 1 << endl;
}