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<stdlib.h>
#include<string.h>
typedef long long ll;
ll dp[55][2600];
int v[55];
int main(void)
{
	int N, A;
	ll sum = 0;
	scanf("%d %d", &N, &A);
	for (int i = 1; i <= N; i++)
		scanf("%d", &v[i]);
	dp[0][0] = 1;
	for (int k = 1; k <= N; k++)
	{
		sum += v[k];
		for (int i = k; i >=1; i--)
			for (int j = sum; j >= v[k]; j--)
				dp[i][j] += dp[i - 1][j - v[k]];
	}
	ll ans = 0;
	for (int i = 1; i <= N; i++)
		ans += dp[i][i * A];
	printf("%lld\n", ans);
	return 0;
}