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 long long ll;

int main(){
	int n,a;
	int x[52];
	scanf("%d%d",&n,&a);
	for(int i = 0 ; i < n ; i ++){
		scanf("%d",&x[i]);
	}
	
	static ll dp[52][2502] = {};
	dp[0][n*a] = 1;
	ll ret = 0;
	for(int i = 0 ; i < n ; i ++){
		ret += dp[i][n*a+a-x[i]];
		for(int j = 0 ; j < 2502 ; j ++){
			dp[i+1][j] = dp[i][j];
		}
		for(int j = 0 ; j < 2502 ; j ++){
			if(0 <= j+x[i]-a && j+x[i]-a < 2502){
				dp[i+1][j+x[i]-a] += dp[i][j];
			}
		}
	}
	cout << ret << endl;
}

