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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;

/**
 * Created by slycer on 1/10/16.
 */
public class kMultipleFreeSet {


    public static void main ( String [] args ) throws IOException {
       FastReader reader = new FastReader();
        reader.nextLineAsInt();
        int n = reader.nextInt();
        int k = reader.nextInt();
        int [] data = reader.nextLineAsInt();
        Arrays.sort( data );
        Set<Integer> answer = new HashSet<>();
        for ( int i : data ){
            if ( i%k == 0 && answer.contains( i/k) ){
            } else {
                answer.add( i );
            }
        }
        System.out.println( answer.size() );
    }

    public static class FastReader {
        private BufferedReader reader;
        private int [] lastLineAsInt;
        private int pos;

        public FastReader (){
            reader = new BufferedReader( new InputStreamReader( System.in ) );
        }
        public long [] nextLineAsLong() throws IOException {
            String [] aux = reader.readLine().split( " " );
            long [] ret = new long[ aux.length ];
            for ( int i=0; i<aux.length; i++ ){
                ret[i] = Integer.valueOf( aux[i] );
            }
            return ret;
        }

        public int [] nextLineAsInt() throws IOException {
            String [] aux = reader.readLine().split( " " );
            int [] ret = new int[ aux.length ];
            for ( int i=0; i<aux.length; i++ ){
                ret[i] = Integer.valueOf( aux[i] );
            }
            pos = 0;
            lastLineAsInt = ret;
            return ret;
        }

        public int nextInt(){
            return lastLineAsInt[pos++];
        }

        public String nextLine() throws IOException {
            return reader.readLine();
        }
    }
    

}
