You won't catch up!
What do you think is the favorite mode of transportation for students? Naturally, it's the bicycle! Bicycles are incredibly beneficial: they're environmentally friendly, provide great exercise to keep you fit, and are a joy to ride with friends. Let's encourage more cycling!
Racing through the city streets in a challenge to see "who can leave the city first" is not only a workout for the legs but also for the mind! Navigating the maze of city streets to find an exit is more challenging than submitting a database project on the first try! You can travel from intersection to intersection, with two-way roads connecting them. These roads might be tunnels, bridges, or regular streets, but for our task, the type doesn't matter. The city has several special intersections that serve as exits to federal highways.
Students Borya and Pasha are passionate cyclists. One day, they made a bet on whether Pavlo could catch up with Boris. The terms of the bet were as follows:
- Pavlo and Boris start from predetermined intersections, knowing each other's starting points. They begin simultaneously. - Boris's goal is to reach any city exit leading to a federal road as quickly as possible. - Pavlo's goal is to catch up with Boris, but he cannot exceed a speed of 160 kilometers per hour. Try pedaling a bicycle at that speed yourself! - Boris wants to ride at the slowest possible speed that still allows him to stay ahead of Pavlo. - If Pavlo and Boris reach the city exit at the same time, Pavlo is considered not to have caught Boris.
Who will win this exciting race?
Input
The input file contains the following information:
- The first line includes three integers: - N - the number of intersections in the city (up to 100), - M - the number of roads (up to 5000), - E - the number of city exits.
- The next M lines each describe a road with three integers: the numbers of the intersections it connects and the road's length in hundreds of meters. No road is longer than 100 hundreds of meters, and no two intersections are connected by more than one road.
- The following line lists E integers, representing the intersections that are city exits.
- The last line contains two integers b and p (1 ≤ b, p ≤ N, b ≠ p), indicating the starting intersections for Borya's and Petya's bicycles.
Output
Output the minimum speed Boris must maintain to win, or print IMPOSSIBLE if Boris cannot win. The result should be accurate to within an absolute or relative error of 10^{-6}. The speed should be expressed in kilometers per hour.