f Naturaliser

By Kay Akashi

Time: 1000 ms

Memory: 256000 kB

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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

Input

3 5 8 4 9 3

Output

-5 -2 1

Explanation

$f(x) = \frac{3x^{2} + 5x + 8}{4x^{2} + 9x + 3}$ . $f(-5) = 1$ , $f(-2) = 10$ , and $f(1) = 2$ . No other value satisfies the condition.

Input

3 3 2 4 3 2

Output

Explanation

It is only $x = 0$ that makes $f(x)$ a positive integer, which is $1$ .

Input

3 3 5 4 5 7

Output

None

Explanation

Be aware that some types of $f(x)$ don't have any $x$ that makes it a positive integer number. In this case, output "None".

f Naturaliser

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