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 Practice3.CF272;

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

public class CF274A {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);

        int n = s.nextInt();
        long k = s.nextLong();
        long[] arr = new long[n];
        HashMap<Long,Integer> map = new HashMap<>();
        for (int i = 0; i < arr.length; i++) {
            arr[i] = s.nextLong();
        }

        Arrays.sort(arr);
        for (int i = 0; i < arr.length; i++) {
            map.put(arr[i],i);
        }
        boolean[] bool = new boolean[n];
        long count = 0;
        for (int i = 0; i < n; i++) {
            if(!bool[i]){
                count++;
                if(map.containsKey(k * arr[i])){
                    int index = map.get(k*arr[i]);
                    bool[index] = true;
                }
            }
        }

        System.out.println(count);
    }
}
