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.*;

public class kultipleFreeSet {

	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];
		for(int i=0;i<n;i++){
			arr[i] = s.nextLong();
		}
		
		Arrays.sort(arr);
		int count=0;
		
		HashSet<Long> hs = new HashSet<Long>();
		for(int i=0;i<n;i++){
			
			if(hs.contains(arr[i]))
				continue;
			
			long nk = arr[i] *k;
			if(Arrays.binarySearch(arr, nk) >=0) {
				hs.add(nk);
				
			}
			count++;
		}
		System.out.println(count);
	}
}
