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.io.*;
import java.util.*;
import java.math.*;

public class Solve {
	public static void main(String[] args) throws FileNotFoundException {
		//Scanner in = new Scanner(new FileReader("input.txt"));
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		long k = in.nextLong();
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = in.nextLong();
		Arrays.sort(a);
		int ans = 0;
		HashSet<Long> s = new HashSet<Long>();
		for(int i = 0; i < n; i++) {
			if (!s.contains(a[i])) {
				ans++;
				s.add(a[i] * k);
			}
		}
		System.out.println(ans);
	}
}