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<algorithm>
using namespace std;
#define MAXN 51
#define LL long long
LL dp[MAXN][MAXN][MAXN],ans;
int main()
{
	int n,A,x;
	scanf("%d%d",&n,&A);
	dp[0][0][0]=1;
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&x);
		for(int m=i-1;m>=0;m--)
			for(int j=0;j<A;j++)
				for(int k=0;k<=n;k++)
					if(k+(j+x)/A<=n)
						dp[(j+x)%A][k+(j+x)/A][m+1]+=dp[j][k][m];
	}
	for(int i=1;i<=n;i++)
		ans+=dp[0][i][i];
	printf("%lld\n",ans);
}