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 java.io.*;
import java.math.*;
public class cf
{
    static int n;
    static int m;
    static Integer arr[];
    public static int bs(int low,int high,long find)
    {
        while(low<=high)
        {
            int mid=(low+high)/2;
            if(arr[mid]==find)
            return mid;
            else if(arr[mid]>find)
            high=mid-1;
            else
            low=mid+1;
        }
        return -1;
    }
    public static void main(String[] args)throws IOException
    {
        PrintWriter out= new PrintWriter(System.out);
        Scanner sc=new Scanner(System.in);
        n=sc.nextInt();
        m=sc.nextInt();
        arr=new Integer[n];
        for(int i = 0 ;i<n;i++)
        arr[i]=sc.nextInt();
        Arrays.sort(arr);
        int mark[]=new int[n];
        int counter=0;
        for(int i = 0 ;i<n;i++)
        {
            if(mark[i]==1)
            continue;
            counter++;
            int pos=bs(i+1,n-1,arr[i]*(long)m);
            if(pos==-1)
            continue;
            mark[pos]=1;
        }
        System.out.println(counter);
    }
}