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

$T=28.2842712$