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>
using namespace std;
long long int a[55][6005];
int main(){
	int n,s;
	int i,j,k;
	int c[52];
	cin>>n>>s;
	for(i=0;i<n;i++){
		cin>>c[i];
		c[i]-=s;
	}
	a[0][3000]=1;
	for(i=0;i<n;i++){
		for(j=0;j<6000;j++){
			if(j-c[i]<0 || j-c[i]>=6000){
				a[i+1][j]=a[i][j];
			}else{
				a[i+1][j]=a[i][j]+a[i][j-c[i]];
			}
		}
	}
	cout<<(a[n][3000]-1)<<endl;
	return 0;
}
