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

Note

In the sample input one of the possible maximum 2-multiple free subsets is {4, 5, 6}.