Description

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

$1 \le A < W \le 1000$

$1 \le B < H \le 1000$

$1 \le A+x_0 \le W$

$1 \le B+y_0 \le H$

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

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

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

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'.

11 11
1 1
5 5
1 1

282842

Note

$T = 28.2842712$