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}.
// package Mathematical;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.HashMap;

public class KMultipleFreeSet {
    public static void main(String[] args)throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        String line[]=br.readLine().split(" ");
        int n=Integer.parseInt(line[0]);
        int k=Integer.parseInt(line[1]);
        line=br.readLine().split(" ");
        int a[]=new int[n];
        for(int i=0;i<n;i++){
            a[i]=Integer.parseInt(line[i]);
        }
        Arrays.sort(a);
        HashMap<Integer,Integer> map=new HashMap<>();
        map.put(a[0],1);
        for(int i=1;i<n;i++){
            if(map.containsKey(a[i]/k)&&a[i]%k==0){
                continue;
            }
            else{
                map.put(a[i],1);
            }
        }
        System.out.println(map.size());
    }
}
