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.*;

import static java.lang.System.*;

public class C275 {
	Scanner sc = new Scanner(in);

	public void run() {
		int n=sc.nextInt();long k=sc.nextInt();
		long[] a=new long[n];
		boolean[] used=new boolean[n];
		for(int i=0;i<n;i++){
			a[i]=sc.nextInt();
		}
		int res=0;
		Arrays.sort(a);
		for(int i=0;i<n;i++){
			if(!used[i]){
				used[i]=true;
				res++;
				long val=a[i];
				int ind=Arrays.binarySearch(a,val*k);
				if(ind>=0){
					used[ind]=true;
				}
			}
		}
		ln(res);
	}

	public static void main(String[] _) {
		new C275().run();
	}

	public static void pr(Object o) {
		out.print(o);
	}
	public static void ln(Object o) {
		out.println(o);
	}
	public static void ln() {
		out.println();
	}
}