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.*;
public class Main{
public static void main (String [] args){
 Scanner in = new Scanner(System.in);
  int n =in.nextInt();
  int k= in.nextInt();
  int array[]= new int [n];
  for(int i=0;i<n;i++){
   array[i]=in.nextInt();
     }
     Arrays.sort(array);
     HashSet<Long> hs=new HashSet<Long>();
      int answer=0;
      
      for(int i=0;i<array.length;i++){
       if(!hs.contains((long)array[i])){
         hs.add((long)array[i]*k);
          answer++;
          }
          }
      System.out.println(answer);
      }
      }
     
     
     
     
     
     
     
     
     
     
  