The Newton brothers are planning to rob a bank in the city
of Alviso and want to figure out a way to escape the city’s
only police car. They know that their car is faster than the
police car so if they could just reach one of the highways
exiting the city they will be able to speed away from the
police.
The police car has a maximum speed of 160 km/h. Luckily, the
brothers know where the police car will start (it’s parked at
the police station). To be on the safe side they assume that
the police car will start moving as soon as they leave the bank
and start their car (this is when the alarm goes off).
The brothers want to find a fixed route that ensures that
they are able to leave the city no matter what route the police
car take and at what speed it drives. However, since the
brothers are not very confident drivers they don’t want to
drive faster than necessary. Luckily they have recently
invested in a new hitech incar police escape system that
you have constructed. This system will tell them what
the minimal top speed needed to escape is (and probably other
useful things like what route to take).
Let’s turn the clock back a bit to the time when you were
constructing the escape system and focused on finding the
minimal required speed. Can you get it right?
You may treat all roads as
infinitesimally narrow and both cars as point objects. If the
brothers ever end up at the same point (on any road or
intersection) at the same time as the police car they will be
caught and by Murphy’s law if there is any possibility of this
happening it will happen. The two cars start simultaneously and
can accelerate/decelerate instantaneously at any time to any
speed below or equal to its maximum speed. They can also change
roads at intersections or direction anywhere on a road
instantaneously no matter what speed they are traveling
at.
Input
The first line of the input consists of three integers
$n$, $m$ and $e$, where $2 \le n \le 100$ describe the number
of intersections, $1 \le m \le
5\, 000$ describes the number of roads in the city and
$1 \le e \le n$ describes
the number of highway exits. Then follow $m$ lines, each consisting of three
integers $a,b,l$ such that
$1 \le a < b \le n$ and
$1 \le l \le 100$
describing a road of length $l$ hundred meters from intersection
$a$ to intersection
$b$. Then follows a line
of $e$ integers, each one
a number in $1, \ldots ,
n$ describing which intersections are connected to
highway exits. Finally there is a line with two integers
$b$ and $p$ ($1
\le b,p \le n \text { and } b \neq p$) describing the
intersections where the brothers and the police cars start,
respectively.
It will always be possible to travel from
any intersection to any other intersection. Roads are only
connected at intersection points (although they may cross using
bridges or tunnels at others points). Roads can be used in both
directions but there cannot be more than one road between two
intersections.
Output
The minimal speed in km/h required to escape or the word
IMPOSSIBLE if it is impossible. In
the first case any answer with either absolute or relative
error smaller than $10^{6}$ is acceptable.
Sample Input 1 
Sample Output 1 
3 2 1
1 2 7
2 3 8
1
3 2

IMPOSSIBLE

Sample Input 2 
Sample Output 2 
3 2 1
1 2 7
2 3 8
1
2 3

74.6666666667

Sample Input 3 
Sample Output 3 
4 4 2
1 4 1
1 3 4
3 4 10
2 3 30
1 2
3 4

137.142857143
