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;
typedef pair<int,int> pi;
typedef long long lint;
const int offset = 2500;

lint dp[55][5005];
int n, a[55];

int main(){
	int x;
	cin >> n >> x;
	for(int i=0; i<n; i++) cin >> a[i], a[i] -= x;
	dp[0][offset] = 1;
	for(int i=0; i<n; i++){
		for(int j=0; j<=2*offset; j++){
			if(j >= a[i]) dp[i+1][j - a[i]] += dp[i][j];
			dp[i+1][j] += dp[i][j];
		}
	}
	cout << dp[n][offset] - 1 << endl;
}
