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>
#define ll long long
#define maxn 55
using namespace std;
ll dp[maxn][maxn*maxn];
int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	int n,A;
	cin >> n >> A;
	
	dp[0][0] = 1;
	for(int i=1,val;i<=n;i++) {
		cin >> val;
		for(int j=i;j>=1;j--) {
			for(int k=val;k<=2500;k++) {
				dp[j][k] += dp[j-1][k-val];
			}
		}	
	}
	ll ans = 0;
	for(int i=1;i<=n;i++)
		ans += dp[i][A*i];
	cout << ans << endl;
	return 0;
}
