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.*;
import java.io.*;
import java.math.*;
public class Class{

    public static void main(String[] args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        TreeSet<Integer> set = new TreeSet<Integer>();
        TreeSet<Integer> setx = new TreeSet<Integer>();
        st = new StringTokenizer(br.readLine());
        for(int i=0; i<n; i++)set.add(Integer.parseInt(st.nextToken()));
        Iterator<Integer> it = set.iterator();
        int sum = n;
        if(k==1){System.out.print(n); return;}
        while(it.hasNext()){
            int j1 = it.next();
            long j = j1;
            if(setx.contains((int)j)==false)
            if(j*k<=1000000000&&set.contains((int)j*k)){setx.add((int)j*k); sum--;}  
        }
        System.out.print(sum);
    }
    
    static class Pair{
        long start;
        long end;
        
        public Pair(long start, long end){
            this.start = start;
            this.end = end;
        }
        
        public int hashCode() {
            return (int)(this.start + this.end);
        }
        
        public boolean equals(Object p){
            if(((Pair)p).start==this.start && ((Pair)p).end==this.end)return true;
            return false;
        }
        
        public String toString(){
            return this.start+" "+this.end;
        }
    }
}