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.HashSet;
    import java.util.Scanner;
    import java.util.Set;
    import java.util.stream.IntStream;
     
    public class C{
    	public static void main( String[] u ){
    		Scanner scanner = new Scanner( System.in );
    		int n = scanner.nextInt( );
    		int k = scanner.nextInt( );
    		int[] a = IntStream.generate( scanner::nextInt ).limit( n ).sorted( ).toArray( );
    		Set<Integer> ans = new HashSet<>( );
    		for( int x : a ){
    			if( x % k == 0 ){
    				if( !ans.contains( x / k ) ) ans.add( x );
    			}else ans.add( x );
    		}
    		System.out.println( ans.size( ) );
    	}
    }