3560: k-Multiple Free Set
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Description
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≤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}.