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.Arrays;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class C {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        Set<Long> cross = new HashSet<Long>();
        int n = scanner.nextInt();
        int k = scanner.nextInt();
        scanner.nextLine();
        long[] element = new long[n];
        for (int i = 0; i <element.length ; i++) {
            element[i] = scanner.nextInt();
        }
        Arrays.sort(element);
        for(Long item : element){
           cross.add(item);
        }
        for(Long item : element){
            if (cross.contains(item)){
                if(cross.contains(item*k)){
                    cross.remove(item*k);
                }
            }
        }
        if (k == 1){
            System.out.println(element.length);
        }else{
            System.out.println(cross.size());
        }
    }
}
