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.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;


public class Main {
    public static void main(String[] args) {
        
Scanner input = new Scanner(System.in);
        
        int x = input.nextInt();
        int y = input.nextInt();
        int[] t = new int[x ];
        int sum =0;
        Map<Integer, Boolean> m = new HashMap<Integer, Boolean>();
        for (int i = 0; i < t.length; i++) {
            t[i]=input.nextInt();
        m.put(t[i], true);
        }
        Arrays.sort(t);
    
    for (int i = t.length-1; i >=0; i--) {
        if(t[i]%y==0){
    boolean v = m.get(t[i]);
    if(v==true){sum++;
        if(m.containsKey(t[i]/y)) m.put((t[i]/y), false);
        
    }
        }else  if(t[i]%y!=0&&m.get(t[i])==true) sum++;
        }
    System.out.println(sum);
    }
    
}
