A9489 | Divisors

Bizon the Champion isn't just friendly, he also is a rigorous coder.

Let's define function $f(a)$ , where $a$ is a sequence of integers. Function $f(a)$ returns the following sequence: first all divisors of $a_{1}$ go in the increasing order, then all divisors of $a_{2}$ go in the increasing order, and so on till the last element of sequence $a$ . For example, $f([2,9,1])=[1,2,1,3,9,1]$ .

Let's determine the sequence $X_{i}$ , for integer $i$ $(i>=0)$ : $X_{0}=[X]$ ( $[X]$ is a sequence consisting of a single number $X$ ), $X_{i}=f(X_{i-1})$ $(i>0)$ . For example, at $X=6$ we get $X_{0}=[6]$ , $X_{1}=[1,2,3,6]$ , $X_{2}=[1,1,2,1,3,1,2,3,6]$ .

Given the numbers $X$ and $k$ , find the sequence $X_{k}$ . As the answer can be rather large, find only the first $10^{5}$ elements of this sequence.

A single line contains two space-separated integers — $X$ $(1<=X<=10^{12})$ and $k$ $(0<=k<=10^{18})$ .

Print the elements of the sequence $X_{k}$ in a single line, separated by a space. If the number of elements exceeds $10^{5}$ , then print only the first $10^{5}$ elements.