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.

Input

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

Output

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.