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;

using int64 = long long;

int64 dp[60][60][2600];

int main() {
	int N, A;
	cin >> N >> A;
	
	int x[50];
	for (int i = 0; i < N; i++) {
		cin >> x[i];
	}
	
	dp[0][0][0] = 1;
	for (int i = 0; i < N; i++) {
		for (int j = 0; j <= i; j++) {
			for (int sum = 0; sum <= 50 * j; sum++) {
				dp[i + 1][j][sum] += dp[i][j][sum];
				dp[i + 1][j + 1][sum + x[i]] += dp[i][j][sum];
			}
		}
	}
	
	int64 ans = 0;
	for (int n = 1; n <= N; n++) {
		ans += dp[N][n][n * A];
	}
	cout << ans << endl;
	
	return 0;
}