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>
#define N 55
using namespace std;

typedef long long ll;
ll n, m, s, a[N], d[N * N][N];
int main()
{
	ll i, j, k;
	cin >> n >> m;
	for (i = 0; i < n; i++) scanf("%lld", &a[i]);
	for (i = 0; i < n; i++) {
		for (j = n * m; j >= a[i]; j--) {
			for (k = 1; k <= i; k++) d[j][k + 1] += d[j - a[i]][k];
		}
		d[a[i]][1]++;
	}
	for (i = 1; i <= n * m; i++) {
		for (j = 1; j <= n; j++) if (m * j == i) s += d[i][j];
	}
	cout << s;
    return 0;
}