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;
long long dp[55][6000];
int main()
{
	int t,p,q;
	scanf("%d%d",&t,&p);
	dp[0][3000]=1;
	for(int i = 0;i < t;i++)
	{
		scanf("%d",&q);
		for(int j = 0;j < 6000;j++)
		{
			if(dp[i][j]!=0 && j+q-p>=0 && j+q-p<6000)
			{
				dp[i+1][j+q-p]+=dp[i][j];
			}
			dp[i+1][j]+=dp[i][j];
		}
	}
	printf("%lld",dp[t][3000]-1);
}