6213: k-Multiple Free Set

内存限制:256 MB 时间限制:2 S
题面:传统 评测方式:文本比较 上传者:
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题目描述

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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}.