You won't catch up!#2244
What do you think is the favorite mode of transportation for students? Of course, it's the bicycle! Bicycles are very beneficial: they are environmentally friendly, provide great exercise, and it is enjoyable to ride with friends. So, let's support cycling!
Racing to see "who will leave the city first" is not only exercise for the legs, but also a workout for the mind! Finding a way out of the city through its complex street maze can be even harder than submitting a database project on the first try! In this city, you can travel from intersection to intersection, connected by two-way roads. These roads may be tunnels, bridges, or ordinary streets, but for this problem, that does not matter. The city contains several special intersections — exits to federal highways.
Borya and Pavel are enthusiastic cycling students. One day, they made a bet: can Pavel catch up to Borya? The terms of the bet are:
Pavel and Borya place their bicycles at predetermined intersections. Each knows where the other starts. They start at the same time.
Borya's task is to reach any city exit at the lowest possible speed.
Pavel's task is to catch up with Borya. However, Pavel's speed cannot exceed kilometers per hour. This is not much of a limitation — try pedaling a bicycle that fast yourself!
Borya does not want to strain himself and intends to travel at the lowest possible speed that still lets him stay ahead of Pavel.
If Pavel and Borya reach a city exit at the same time, Pavel is considered not to have caught Borya.
Who will win?
The input file contains the following data:
The first line contains three integers:
— the number of intersections in the city (at most ),
— the number of roads (at most ),
— the number of city exits.
The next lines each describe a road by three integers: the numbers of the intersections it connects, and the length of the road in hundreds of meters. Any road is at most hundreds of meters long. No two intersections are connected by more than one road.
The next line contains integers — the indices of intersections that are city exits.
The last line contains two integers and (1 \leq b,\ p \leq N, b \neq p) — the intersections where Borya's and Pavel's bicycles are initially placed.
Output either the minimal speed at which Borya must travel to win, or the word IMPOSSIBLE if Borya cannot win. The result should be printed with an absolute or relative error not exceeding 10^{-6}. The speed must be given in kilometers per hour.
Example 1