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.PrintWriter;
import java.util.*;

public class KMultipleFreeSet {
	
	static long[] set = new long[100000];
	static int[] multiples = new int[100000];
	static int[] ret = new int[100000];
	
	public static void main(String[] args) {		
		
		int r;
		
		int n = 0;
		int k;		
		
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		k = sc.nextInt();
		for (int i = 0; i < n; i++) {
			set[i] = sc.nextInt();
		}
		
		PrintWriter pw = new PrintWriter(System.out);
		if(n>0) {
			r = maxSet(set, n, k);		
			pw.println(r);
			pw.flush();
		}
	}

	private static int maxSet(long[] set, int n, int k) {
		
		Arrays.sort(set, 0, n);		
		for (int i = 0; i < n; i++) {
			multiples[i] = Arrays.binarySearch(set, 0, n, set[i]*k);
			ret[i] = 1;
		}
		
		int count = 0;
		for (int i = 0; i < n; i++) {
			if(multiples[i]<0 && ret[i]>0)
				count++;
			else if(multiples[i]>=0 && ret[i]>0) {
				ret[multiples[i]] = -1;
				count++;
			}
		}
		return count;
	}
}