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 <iostream>
#include<vector>
using namespace std;

int main() {
	long long n,a;cin>>n>>a;
	vector<long long> x(n);
	for(int i=0;i<n;i++){
		cin>>x[i];
		x[i]-=a;
	}
	vector<long long> v(50*51,0);
	vector<long long> v2(50*51,0);
	int def=50*26;
	v2[def]++;
	v2[def+x[0]]++;
	v=v2;

	for(int i=1;i<n;i++){
		for(int j=0;j<50*51;j++){
			v2[j+x[i]]+=v[j];
		}
		v=v2;
	}
	cout<<v[def]-1<<endl;
//	for(int i=def-30;i<def+30;i++){
//		cout<<v[i]<<endl;
//	}
	return 0;
}
