At coding club, Darcy is watching the bouncing screensaver meme. The screensaver consists of rectangular DVD logo of width and height bouncing around a rectangular screen of width and height at a speed of 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 (measured from the bottom left corner of the screen and logo) and travels in the direction . After a while, Darcy noticed that the logo returned to it's starting position and velocity. What is the minimum time Darcy had to wait?
The first line contains integers and , the width and height of the screen.
The second line contains integers and , the width and height of the logo.
The third line contains integers and , 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 and , meaning the logo has the same initial direction as an vector pointing units right and units up.
Let be the minimum amount of seconds after beginning such that the logo is at position travelling in direction . Print the 6 digits beginning from the first non-zero digit of .
If this will never happen, print
Subtask 1 [20%]
11 11 1 1 5 5 1 1