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.*;
public class k_MultipleFreeSet{
    public static void main(String[]args){
        Scanner input = new Scanner(System.in);
        long[] a = new long[input.nextInt()];
        boolean[] b = new boolean[a.length];
        long k = input.nextInt();
        for(int i = 0; i < a.length; i++)
            a[i] = input.nextInt();
        Set<Long> s = new HashSet<Long>();
        int c = 0;
        Arrays.sort(a);
        for(int i = 0; i < a.length; i++)
            if(!s.contains(a[i])){
                s.add(a[i] * k);
                c++;
            }

        System.out.println(c);
    }
}