A k-multiple free set is a set of integers where there is no pair of integers where one is equal to another integer multiplied by k. That is, there are no two integers x and y (x < y) from the set, such that y = x·k.

You're given a set of n distinct positive integers. Your task is to find the size of it's largest k-multiple free subset.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 105, 1 ≤ k ≤ 109). The next line contains a list of n distinct positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

All the numbers in the lines are separated by single spaces.

Output

On the only line of the output print the size of the largest k-multiple free subset of {a1, a2, ..., an}.

Examples

Input

6 2
2 3 6 5 4 10


Output

3

Note

In the sample input one of the possible maximum 2-multiple free subsets is {4, 5, 6}.
import	java.util.*;
public	class	Main{
	public	static	void	main(String[]args){
		Scanner	cin=new	Scanner(System.in);
		int	n,m,i,j,k,Q[]=new	int[100000];
		for(boolean[]F=new	boolean[100000];cin.hasNextInt();System.out.println(n)){
			for(j=n=cin.nextInt(),m=cin.nextInt();0<j;F[j]=true)
				Q[--j]=cin.nextInt();
			if(1<m)	for(Arrays.sort(Q,0,i=n);Q[j]<=Q[--i]/m;)
				if(F[i]&&0==Q[i]%m&&-1<(k=Arrays.binarySearch(Q,j,i,Q[i]/m))){
					--n;
					if(j==k)	++j;
					else	if(i-2<k)	--i;
					else	F[k]=false;
				}
		}
	}
}
