f Naturaliser

By Kay Akashi

Problem Statement

Given $6$ positive integers $a_{1}$, $b_{1}$, $c_{1}$, $a_{2}$, $b_{2}$, and $c_{2}$, you will think of a function $f(x) = \frac{a_{1}x^{2} + b_{1}x + c_{1}}{a_{2}x^{2} + b_{2}x + c_{2}}$.

Your task is to find all $x$ such that $f(x)$ is a positive integer. ($x$ is an integer). 0 is not a positive integer.

It is ensured that $a_{1} \lt a_{2}$.

Constraints

$1 \leq a_{1}, b_{1}, c_{1}, a_{2}, b_{2}, c_{2}, \leq 10$. $a_{1} \lt a_{2}$.

Input

The input consists of 6 integers, $a_{1}$, $b_{1}$, $c_{1}$, $a_{2}$, $b_{2}$, and $c_{2}$, in a single line.

Output

List the possible $x$ in one line, in an increasing order. If there's no such $x$, output "None" instead.

Examples

3 5 8 4 9 3

-5 -2 1

3 3 2 4 3 2

0

3 3 5 4 5 7

None