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

public class Task {
	
	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		/**
		 * ########################
		 * Solution
		 */
		
		int n = sc.nextInt();
		int k = sc.nextInt();
		
		long[] a = new long[n];
		boolean[] d = new boolean[n];
		
		for(int i = 0; i < n; i++)
		{
			a[i] = sc.nextInt();
		}
		
		Arrays.sort(a);
		
		int count = 0;
		
		for(int i = 0; i < n; i++)
		{
			if(d[i])
				continue;
			long b = a[i]*k;
			int j = Arrays.binarySearch(a, b);
			if(j >= 0)
			{
				d[j] = true;
			}

			count++;
		}
		
		out.println(count);
		
		/**
		 * Solution
		 * ########################
		 */	
		
		out.flush();
	}
}