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;

const int C = 50 * 50 + 5;
int n, m;
long long dp[55][2 * 55 * 55];

int main() {
	scanf("%d%d", &n, &m);

	for(int i = 1; i <= n; i++) {
		int x; scanf("%d", &x);
		x -= m;

		for(int j = 50 * 50; j >= -50 * 50; j--) {
			if(j - x <= 50 * 50 && j - x >= -50 * 50) {
				dp[i][j + C] += dp[i - 1][j - x + C];
				dp[i][j + C] += dp[i - 1][j + C];
			}
		}

		dp[i][x + C]++;
	}

	printf("%lld\n", dp[n][C]);
	return 0;
}