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;

int x[100];
long long dp[100][2500];

int main() {
	int n, A, s = 0;
	scanf("%d%d", &n, &A);
	for(int i = 0; i < n; i++) scanf("%d", x + i), s += x[i];
	dp[0][0] = 1;
	for(int i = 1; i <= n; i++)
		for(int k = n; k >= 0; k--)
			for(int j = s; j >= 0; j--)
				if(j - x[i-1] >= 0) dp[k + 1][j] += dp[k][j - x[i-1]];
	long long res = 0;
	for(int i = 1; i <= n; i++) res += dp[i][A * i];
	printf("%lld\n", res);
	return 0;
}
