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;

long long n, a, ans, x[100], w[5000][100];
int main(){
	cin >> n >> a;
	w[0][0] = 1;
	for(int i = 0; i < n; i++){
		cin >> x[i];
		for(int j = 1; (j*a-x[i]) <= 3000; j++){
			if(j*a-x[i] >= 0) ans += w[j*a-x[i]][j-1];
		}
		for(int j = 100; j >= 1; j--){
			for(int k = 3000; k >= x[i]; k--){
				w[k][j] += w[k-x[i]][j-1];
			}
		}
	}
	cout << ans;
}