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 final class KMultipleFreeSet {
    public static  int MAX= (int) Math.pow(10,9);
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int k=sc.nextInt();
        int arr[]=new int[n];
        for(int i=0;i<n;i++){
            arr[i]=sc.nextInt();
        }
        Arrays.sort(arr);
        HashSet<Integer> set=new HashSet<>();
        for(int i=0;i<n;i++){
            if(arr[i]%k==0){
                if(!set.contains(arr[i]/k)){
                    set.add(arr[i]);
                }
            }else{
                set.add(arr[i]);
            }
        }
        System.out.println(set.size());
    }
    
}
