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.lang.*;
import java.util.*;

public final class Solution {
    public static void main(String[] args) {
        Solution program = new Solution();
        program.run();
    }
    
    private void run() {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }
        Arrays.sort(a);
        HashSet<Integer> hs=new HashSet<Integer>();
        for (int i = 0; i < n; i++) {
        	if (a[i]%k != 0) {
        		hs.add(a[i]);
        	} else if (!hs.contains(a[i]/k)) {
    			hs.add(a[i]);
        	}
        }
        System.out.println(hs.size());
    }
    
    
}