Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. k-Multiple Free Set

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA *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* ≤ 10^{5}, 1 ≤ *k* ≤ 10^{9}). The next line contains a list of *n* distinct positive integers *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{9}).

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 {*a*_{1}, *a*_{2}, ..., *a*_{n}}.

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}.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/20/2019 15:39:08 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|