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>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
long long dp[2][5050];
int main()
{
	int n,a,now,to,x;
	scanf("%d%d",&n,&a);
	memset(dp,0,sizeof(dp));
	now=0;
	to=1;
	dp[0][2500]=1;
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&x);
		x-=a;
		for(int j=0;j<=5000;j++)
			if(dp[now][j])
			{
				dp[to][j]+=dp[now][j];
				dp[to][j+x]+=dp[now][j];
				dp[now][j]=0;
			}
		swap(now,to);
	}
	printf("%lld",dp[now][2500]-1);
	return 0;
}