【Codeforces】[274A]k-Multiple Free Set

Description

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 $k$ ($1 ≤ n ≤ 10^{5}, 1 ≤ k ≤ 10^{9}$). 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}.