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>

long long dp[51][51][2501], x[51], n, A;

int main () {
	dp[0][0][0] = 1;
	std::cin >> n >> A;
	for (int i = 1; i <= n; ++i) std::cin >> x[i];
	for (int i = 0; i < n; ++i) {
		for (int j = 0; j <= i; ++j) {
			for (int k = 0; k <= 2500-x[i+1]; ++k) {
				if (!dp[i][j][k]) continue;
				dp[i+1][j+1][k+x[i+1]] += dp[i][j][k];
				dp[i+1][j][k] += dp[i][j][k];
			}
		}
	}
	long long ans = 0;
	for (int i = 1; i <= n; ++i) ans += dp[n][i][A*i];
	std::cout << ans << "\n";
	return 0;
}