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;
using ll = long long;
int main() {
	int n, A;
	cin >> n >> A;
	vector<int> a(n);
	for(int i = 0; i < n; ++i) {
		cin >> a[i];
	}
	vector<vector<ll> > dp;
	dp.assign(n + 1, vector<ll> ());
	for(int i = 0; i <= n; ++i) {
		dp[i].assign(5005, 0);
	}
	dp[0][2500] = 1;
	for(int i = 0; i < n; ++i) {
		int x = a[i] - A;
		for(int j = 0; j <= 5000; ++j) {
			dp[i + 1][j] += dp[i][j];
			if(j + x >= 0) {
				dp[i + 1][j + x] += dp[i][j];
			}
		}
	}
	cout << dp[n][2500] - 1  << '\n';
	return 0;
}