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 Specification

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.

Output Specification

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.

Constraints

~1 \le A < W \le 1000~
~1 \le B < 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~

Sample Input

11 11
1 1
5 5
1 1

Sample Output

282842

Explanation

~T = 28.2842712~