That went well! As police sirens rang out around the palace,
Mal Reynolds had already reached his lifting device outside of
the city.
No spaceship can escape Planet Zarzos without permission
from the High Priest. However, Mal’s spaceship, Firefly, is in
geostationary orbit well above the controlled zone and his
small lifting device can avoid being recognised as an intruder
if its vertical velocity is exactly $1$ km/min.
There are still two problems. First, Mal will not be able to
control the vehicle from his space suit, so he must set up the
autopilot while on the ground. The vertical velocity must be
exactly $1$ km/min and the
horizontal velocity must be set in such a way that Mal will hit
the Firefly on the resulting trajectory. Second, the energy
shields of the planet disturb the autopilot: They will decrease
or increase the horizontal velocity by a given factor. The
original horizontal velocity is restored as soon as there is no
interference. For this problem we consider Firefly to be a
single point – the shape shown in Figure 1 is merely for
decorative purposes.
Luckily, Mal recorded the positions of the shields and their
influence on the autopilot during his descent. What he needs
now is a program telling him the right horizontal velocity
setting.
Input
The input consists of:

one line with two integers $x$, $y$ ($10^7 \le x \le 10^7$,
$x \le y \le 10^8$
and $1 \le y$),
Firefly’s coordinates relatively to Mal’s current position
(in kilometres).

one line with an integer $n$ ($0 \le n\le 100$), the number of
shields.

$n$ lines
describing the $n$
shields, the $i$th
line containing three numbers:

an integer $l_
i$ ($0 \le l_ i
< y$), the lower boundary of shield
$i$ (in
kilometres).

an integer $u_
i$ ($l_ i < u_
i \le y$), the upper boundary of shield
$i$ (in
kilometres).

a real value $f_
i$ ($0.1 \le f_ i
\le 10.0$), the factor with which the horizontal
velocity is multiplied during the traversal of shield
$i$.
It is guaranteed that shield ranges do not intersect,
i.e., for every pair of shields $i \ne j$ either $u_ i\le l_ j$ or $u_ j\le l_ i$ must hold.
All real numbers will have at most $10$ digits after the decimal
point.
Output
Output the horizontal velocity in km/min which Mal must
choose in order to reach Firefly. The output must be accurate
to an absolute or relative error of at most $10^{6}$.
Sample Input 1 
Sample Output 1 
100 140
1
40 90 0.2000000000

1.0

Sample Input 2 
Sample Output 2 
100 100
3
0 20 2.0000000000
50 100 0.1000000000
20 50 0.2000000000

1.96078431373
