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.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class a {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n=in.nextInt();
        int k = in.nextInt();
        int a[]=new int[n];
        for(int a0 = 0; a0 < n; a0++){
             a[a0] = in.nextInt();
        }
        Arrays.sort(a);
      int b[]=new int[n];
        for(int i=0;i<n;i++){
            if(b[i]!=-1){
                int l=binarySearch(a,(long)a[i]*k);
                if(l!=-1){
                    b[l]=-1;
                }
            }
        }
        int sum=0;
        for(int i=0;i<n;i++){
            if(b[i]!=-1)
                sum++;
           // System.out.println(b[i]);
        }
        if(k==1)
            sum=n;
            System.out.println(sum);
    }
    public static int  binarySearch(int data[],long key) 
    {
         int low = 0;
         int high = data.length - 1;
          
         while(high >= low) {
             int middle = (low + high) / 2;
             if(data[middle] == key) {
                 return middle;
             }
             if(data[middle] < key) {
                 low = middle + 1;
             }
             if(data[middle] > key) {
                 high = middle - 1;
             }
        }
        return -1;
    }
}
