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;

const int N = 5500;

long long dp[55][N];

int main() {
	
	ios::sync_with_stdio(0);
	cin.tie(0), cout.tie(0);
	
	int n, A; cin >> n >> A;
	dp[0][0] = 1;
	for (int i = 1; i <= n; i++) {
		int x; cin >> x;
		for (int j = i; j >= 1; j--) {
			for (int s = N - 1; s >= 0; s--) if (dp[j - 1][s]) {
				if (s + x < N) dp[j][s + x] += dp[j - 1][s];
			}
		}
	}
	
	long long ans = 0;
	for (int i = 1; i <= n; i++) ans += dp[i][A * i];
	cout << ans << "\n";
	
	return 0;
}
