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 <cstdio>
#include <cstring>
#define N 55
using namespace std;

typedef long long ll;
ll n, m, i,a[N], s[N][N][2505];
ll f(ll p, ll q,ll w) {
	if (p == n) return (q >0 && q * m == w ? 1 : 0);
	if (s[p][q][w] != -1) return s[p][q][w];
	return s[p][q][w] = f(p + 1, q, w) + f(p + 1, q + 1, w + a[p]);
}
int main()
{
	cin >> n >> m;
	for (i = 0; i < n; i++) {
		scanf ("%lld", &a[i]);
	}
	memset(s, -1, sizeof(s));
	cout << f(0, 0, 0);
    return 0;
}