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<stdio.h>
#include<vector>
#include<algorithm>
using namespace std;
typedef long long ll;
ll dp[51][5001];
int main()
{
	int num, mok;
	scanf("%d%d", &num, &mok);
	dp[0][2500] = 1;
	for (int i = 0; i < num; i++)
	{
		int z;
		scanf("%d", &z);
		z -= mok;
		for (int j = -2500; j <= 2500; j++)
		{
			if (-2500 <= j + z&&j + z <= 2500)
			{
				dp[i + 1][j + z + 2500] += dp[i][j + 2500];
			}
			dp[i + 1][j + 2500] += dp[i][j + 2500];
		}
	}
	printf("%lld\n", dp[num][2500] - 1);
}