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;
#define ll long long
#define f(i,x,n) for (int i = x;i < n;++i)

ll d[2501][51];

int main() {
	int n, k;
	scanf("%d%d", &n, &k);
	d[0][0] = 1;
	f(i, 0, n) {
		int t;
		scanf("%d", &t);
		for (int j = 50; j > 0; --j) {
			f(i, t, 2501)d[i][j] += d[i - t][j - 1];
		}
	}
	ll an = 0;
	int i = 1, t = k;
	while (i < 51 && k < 2501) {
		an += d[k][i];
		k += t;
		++i;
	}
	printf("%lld", an);
}