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 <iostream>
#include <cstdio>
using namespace std;
long long n, a, x, s, d[55][2505]={1};
int main() {
	int i, j, k;
	cin>>n>>a;
	for(i=1; i<=n; i++) {
		cin>>x;
		for(j=i; j; j--) 
			for(k=0; k<=(j-1)*50; k++) d[j][k+x] += d[j-1][k];
	}
	for(j=1; j<=n; j++) s += d[j][j*a];
	cout<<s;
	return 0;
}