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 <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long ll;
const int N=2550;
ll f[6007][57]={0};
int n,a,num[57];
int main()
{
	scanf("%d%d",&n,&a);
	for (int i = 1; i <= n; ++i)
	{
		int x;
		scanf("%d",&x);
		num[i]=x-a;
	}
	for (int i = 1; i <= n; ++i)
	{
		for (int j = 55; j < 5057; ++j)
		{
			f[j][i]+=f[j][i-1];
			f[j+num[i]][i]+=f[j][i-1];
		}
		f[N+num[i]][i]++;
	}
	printf("%lld\n", f[N][n]);
	return 0;
}