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 N = 2500;

long long f[51][N + 10];
int n, m;

int main() {
	scanf("%d%d", &n, &m);
	f[0][0] = 1;

	long long ans = 0;
	
	for (int i = 1; i <= n; ++i) {
		int a;
		scanf("%d", &a);
		for (int j = n; j >= 1; --j) {
			for (int k = N; k >= a; --k) {
				f[j][k] += f[j - 1][k - a];
			}
		}
	}
	
	for (int i = 1; i <= n; ++i) {
		ans += f[i][i * m];
	}
	
	printf("%lld", ans);
	return 0;
}