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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 2010-2021 Mike Mirzayanov

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