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.Arrays;
import java.util.HashSet;
import java.util.Scanner;


public class B_168 {
public static void main(String[] args) {
	Scanner sc = new Scanner(System.in);
	int n =sc.nextInt();
	long a[]=new long [n+1];
	long k =sc.nextInt();
	HashSet<Long> set=new HashSet<Long>();
	for (int i = 1; i <=n; i++) {
		a[i]=sc.nextLong();
	}
	Arrays.sort(a,1,n+1);
	int x = 0;
	for (int i = 1; i <=n ; i++) {
	if(!set.contains(a[i])){
		set.add(k*a[i]);
	  x++;
	}
	}
	
	System.out.println(x);
}
}
