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>
using namespace std;

long long dp[55][2505], ans;
int n, a, m;
int main() {
	scanf("%d%d", &n, &a); 
	dp[0][0] = 1; 
	m = a * n;
	for (int t, i = 1; i <= n; i++) {
		scanf("%d", &t);
		for (int j = i; j; --j)
			for (int k = m; k >= t; --k)
				dp[j][k] += dp[j-1][k-t];
	} 
	for (int i = 1; i <= n; ++i) ans += dp[i][i*a];
	printf("%lld\n", ans);
	return 0;
}