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 n, A;
int a[51];
long long ways[51][11000];

int main() {
	scanf("%d %d", &n, &A);
	for (int i = 0; i < n; i++){
		scanf("%d", &a[i]); 
		a[i] -= A;
	}
	ways[0][5000] = 1;
	for (int i = 0; i < n; i++){
		for (int w = -2500; w <= 2500; w++) {
			ways[i + 1][w + 5000] += ways[i][w + 5000];
			ways[i + 1][w + 5000] += ways[i][w + 5000 - a[i]];
		}
	}
	printf("%lld\n", ways[n][5000] - 1);
}
