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;
const int MAXN=51,ZERO=2550;
typedef long long ll;
int n,a,x,cur;
ll dp[2][2*ZERO];

int main() 
{
	scanf("%d%d",&n,&a);
	dp[cur^1][ZERO]=1;
	for (int i=1;i<=n;i++,cur^=1)
	{
		scanf("%d",&x);x-=a;
		for (int j=MAXN;j+MAXN<2*ZERO;j++)
			dp[cur][j]=dp[cur^1][j]+dp[cur^1][j-x];
	}
	printf ("%lld\n",dp[cur^1][ZERO]-1);
}