Yraglac wants to get around within his gated community on
Mars, Cossin. The Cossin community grounds are precisely – but
strangely – shaped. Yraglac has spent many hours studying the
grounds and has figured out the logic behind the
landscaping.
If you put the landscaper’s house on a cartesian grid at
position $(0,0)$, then the
height of the land at each point is equal to $h = \sin \left(\frac{\pi x}{a}\right) \cdot
\cos \left(\frac{\pi y}{b} + \frac{\pi }{2}\right)$ for
some $a$ and $b$ that Yraglac is still working on
figuring out. Roads are laid out wherever the height is
zero.
Yraglac can drive on the roads, but has to walk through any
area that isn’t a road. He doesn’t like walking much, so while
walking he takes the shortest possible path between an offroad
point and the nearest road, breaking ties by whichever makes
his driving shorter.
Given coordinates that Yraglac wants to travel to and from,
can you tell how far Yraglac will have to travel?
Input
The input begins with an integer $1 \leq T \leq 1\, 000$, the number of
test cases.
Each test case contains six integers $a$, $b$, $x_1$, $y_1$, $x_2$, and $y_2$. $a$ and $b$ ($1
\leq a,b \leq 10^8$) are the parameters to the height
calculations, and $(x_1,
y_1)$ and $(x_2,
y_2)$ ($10^8 \leq x_1,
y_1, x_2, y_2 \leq 10^8$) are the starting and ending
positions of Yraglac’s travel, respectively.
You may assume that there is a road intersecting the line
segment from the starting position to the ending position.
Output
The output consists of one number for each test case, the
shortest distance Yraglac has to travel, rounded to the nearest
integer.
Sample Input 1 
Sample Output 1 
2
1 1 0 0 1 1
2 2 1 1 2 2

2
2
