Description

Source: BIO 1997 Round 1 Question 3

In ancient Egypt, people used sums of unit fractions (of the form $\dfrac{1}{a}$, where $a$ is a natural number) to represent all rational numbers. For example: $\dfrac{2}{3} = \dfrac{1}{2} + \dfrac{1}{6}$, but $\dfrac{2}{3} = \dfrac{1}{3} + \dfrac{1}{3}$ is not allowed because the addends are identical. For a fraction $\dfrac{a}{b}$, there are many ways to represent it, but which one is the best? First, a representation with fewer addends is better than one with more. Second, among representations with the same number of addends, the one with the largest smallest fraction is preferred. For example:

$$\begin{aligned} \frac{19}{45} &= \frac{1}{3} + \frac{1}{12} + \frac{1}{180}\\ \frac{19}{45} &= \frac{1}{3} + \frac{1}{15} + \frac{1}{45}\\ \frac{19}{45} &= \frac{1}{3} + \frac{1}{18} + \frac{1}{30}\\ \frac{19}{45} &= \frac{1}{4} + \frac{1}{6} + \frac{1}{180}\\ \frac{19}{45} &= \frac{1}{5} + \frac{1}{6} + \frac{1}{18}\\ \end{aligned} $$

The best representation is the last one because $\dfrac{1}{18}$ is larger than $\dfrac{1}{180}, \dfrac{1}{45}, \dfrac{1}{30}, \dfrac{1}{18}$.
Note that there may be multiple optimal solutions. For example:

$$\begin{aligned} \frac{59}{211} &= \frac{1}{4} + \frac{1}{36} + \frac{1}{633} + \frac{1}{3798}\\ \frac{59}{211} &= \frac{1}{6} + \frac{1}{9} + \frac{1}{633} + \frac{1}{3798}\\ \end{aligned} $$

Since the smallest fractions in the first and second methods are the same, both are considered optimal solutions.

Given $a$ and $b$, write a program to compute the best representation. It is guaranteed that the optimal solution satisfies: the smallest fraction $\ge \cfrac{1}{10^7}$.

Input Format

One line containing two integers, the values of $a$ and $b$.

Output Format

Output several numbers, arranged in ascending order, representing the denominators of the unit fractions.

Sample 1

19 45

5 6 18

Constraints and Hints

$0 \lt a \lt b \lt 1000$