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.HashMap;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Scanner;

public class Flab {
	
	
	/// from editorial
	
	public static void main(String[] args) {
		
		Scanner in = new Scanner(System.in);
		
		int n = in.nextInt();
		int k = in.nextInt();
		
		Map<Integer, Integer> map = new HashMap<>();
		
		int[] arr = new int[n];
		
		for(int i=0; i<n; i++) {
			int d = in.nextInt();
			arr[i] = d;
		}
		
		Arrays.sort(arr);
		
		for(int i=0; i<n; i++) {
			if(arr[i] % k == 0) {
				
				if(map.containsKey(arr[i] / k)) {
					map.put(arr[i], map.get(arr[i]/k) + 1);
					
					map.remove(arr[i]/k);
				}
				else {
					map.put(arr[i], 1);
				}
			}
			else {
				map.put(arr[i], 1);
			}
		}
		
		
		long ans = 0;
		
		for(Entry<Integer, Integer> e : map.entrySet()) {
			int val = e.getValue();
			
			if(val % 2 == 1) {
				val++;
			}
			
			ans += (val/2);
		}
		
		System.out.println(ans);
		
		

		
		
	}
	
}