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;
import java.util.Set;
import java.util.TreeSet;
public class Main {

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		Long k = s.nextLong();
		long []a = new long[n]; 
		
		Set<Long> conjunto=new TreeSet<Long>();

		for (int i = 0; i < n; i++) {
			a[i] = s.nextLong();
		}
		Arrays.sort(a);
		for(int j=a.length-1;j>=0;j--)
		{
			if(!conjunto.contains(a[j]*k))
				conjunto.add(a[j]);
			
		}
		System.out.println(conjunto.size());
	}


}