E. Coding Club
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

At coding club, Darcy is watching the bouncing screensaver meme. The screensaver consists of a rectangular DVD logo of width $$$A$$$ and height $$$B$$$ bouncing around a rectangular screen of width $$$W$$$ and height $$$H$$$ at a speed of $$$1$$$ unit/second. When the logo touches a side of the screen, it bounces off such that the angle of incidence equals the angle of reflection. When the logo reaches a corner, its direction is simply reversed.

The logo begins at position $$$(x_0,y_0)$$$ (measured from the bottom left corner of the screen and logo) and travels in the direction $$$(x,y)$$$. After a while, Darcy noticed that the logo returned to its starting position and velocity. What is the minimum time Darcy had to wait?

Input

The first line contains integers $$$W$$$ and $$$H$$$, the width and height of the screen. The second line contains integers $$$A$$$ and $$$B$$$, the width and height of the logo. The third line contains integers $$$x_0$$$ and $$$y_0$$$, representing the starting position of the logo (measured from the bottom left corner of the screen to the bottom left corner of the logo). The last line contains integers $$$x$$$ and $$$y$$$, meaning the logo has the same initial direction as a vector pointing $$$x$$$ units right and $$$y$$$ units up.

## Constraints

$$$1 \le A \lt W \le 1000$$$

$$$1 \le B \lt H \le 1000$$$

$$$1 \le A+x_0 \le W$$$

$$$1 \le B+y_0 \le H$$$

$$$-10^5 \le x,y \le 10^5$$$

$$$x \ne 0$$$ or $$$y \ne 0$$$

### Subtask 1 [20 $$$1 \le W,H,x,y \le 15$$$

Output

Let $$$T$$$ be the minimum amount of seconds after beginning such that the logo is at position $$$(x_0,y_0)$$$ travelling in direction $$$(x,y)$$$. Print the 6 digits beginning from the first non-zero digit of $$$T$$$.

If this will never happen, print '-1'.

Example
Input
11 11
1 1
5 5
1 1
Output
282842
Note

$$$T = 28.2842712$$$