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;
ll dp[55][3000], x[55];
int main(){
	int n, a;
	cin >> n >> a;
	for(int i = 0; i < n; i ++){
		cin >> x[i];
	}
	dp[0][0] = 1;
	for(int i = 0; i < n; i ++){
		for(int cnt = n; cnt >= 0; cnt --){
			for(int sum = 3000; sum >= 0; sum --){
				if(!dp[cnt][sum]) continue;
				dp[cnt + 1][sum + x[i]] += dp[cnt][sum];
			}
		}
	}
	ll ans = 0;
	for(int i = 1; i <= n; i ++) ans += dp[i][i * a];
	cout << ans << '\n';
	return 0;
}
