Speedy Escape

The Newton brothers have just robbed a bank in the city of Alviso and want to find a way to escape the city's only police car. Their own car is faster than the police car, so if they can reach any of the highways leaving the city they will be able to speed away and get free.

The police car has a maximum speed of 160 km/h. The brothers know where the police car starts (it is parked at the police station). To be safe, they assume the police car starts moving the instant they leave the bank and start their engine (the moment the alarm goes off).

The brothers want to commit to a single fixed route that guarantees they can leave the city no matter which route the police car takes or how fast it drives. Because they are not confident drivers, they also do not want to drive any faster than necessary. Compute the minimal top speed the brothers' car needs in order to guarantee an escape.

Treat every road as infinitesimally narrow and both cars as point objects. If the brothers are ever at the same point (on a road or at an intersection) at the same time as the police car, they are caught; by Murphy's law, if being caught is at all possible it will happen. Both cars start at the same instant and may accelerate or decelerate instantaneously at any time to any speed up to their maximum. They may also switch roads at intersections, or reverse direction anywhere on a road, instantaneously and at any speed.

The first line contains three integers $n$, $m$ and $e$, where $2 \le n \le 100$ is the number of intersections, $1 \le m \le 5000$ is the number of roads, and $1 \le e \le n$ is the number of highway exits.

Each of the next $m$ lines contains three integers $a$, $b$ and $l$ with $1 \le a < b \le n$ and $1 \le l \le 100$, describing a road of length $l$ (in hundreds of meters) connecting intersections $a$ and $b$.

The next line contains $e$ integers, each an intersection (from $1$ to $n$) that is connected to a highway exit.

The final line contains two integers $b$ and $p$ with $1 \le b, p \le n$ and $b \ne p$, the intersections where the brothers and the police car start, respectively.

It is always possible to travel between any two intersections. Roads meet only at intersections (elsewhere they may cross via bridges or tunnels). Every road can be driven in both directions, and there is at most one road between any pair of intersections.

Print the minimal top speed in km/h that the brothers' car needs in order to guarantee an escape, or the word IMPOSSIBLE if no route can guarantee it.

The required speed is always a rational number (it equals 160 times a ratio of two integer distances), so print it as an exact value: as a reduced fraction p/q in lowest terms when it is not an integer, or as the integer p when it is a whole number. If the brothers already start at a highway exit, the required speed is 0.