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.Map;
import java.util.Scanner;
import java.util.TreeMap;

public class KMultiple {

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        
        
        long k, n, number;
        long inf;
        n = scan.nextLong();
        k = scan.nextLong();
        long total = 0;
        TreeMap<Long, Long> lleerlo = new TreeMap<>();
        TreeMap<Long, Long> map = new TreeMap<>();
        for(long i=0;i<n;i++){
            number = scan.nextLong();
            lleerlo.put(number,number);
        }
       for(Map.Entry<Long, Long> entry : lleerlo.entrySet()) {
         number = entry.getKey();
            inf = number/k;
            if(number%k != 0){
                map.put(number, number);
                total +=1;
            }else if(map.get(inf)==null){
                total += 1;
                map.put(number, number);
            }
        }
        System.out.print(total);
    }
    
}