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<cstring>
using namespace std;

typedef long long ll;
const int N = 55;

ll n, A, a[N], mm[N][N][N * N];

ll dp(int i, int cnt, int sum) {
	if (i == n) {
		if (cnt == 0)return 0;
		if ((sum / cnt) == A && (sum % cnt == 0))return 1;
		return 0;
	}

	ll& ret = mm[i][cnt][sum];
	if (ret != -1)return ret;
	return ret = dp(i + 1, cnt, sum) + dp(i + 1, cnt + 1, sum + a[i]);
}

int main() {
	cin >> n >> A;
	for (int i = 0; i < n; i++)cin >> a[i];
	memset(mm, -1, sizeof mm);
	cout << dp(0, 0, 0) << endl;

	return 0;
}