The game of trains

Juan has a new game of trains. This one has varios straight stretches
that can be joined to form longer tracks. Those ones will be joined
always in a way that the track is continuous and all the stretches form
a straight line with different difference of level (the game does not
have curved stretches, these one come with the exapansion). The game
also has carriages that Juan can launch from a point of the rail with
the speed that he wants. Maria, the sister of Juan, has placed the
stretches forming a rail and dares Juan to launch a carriage from the
beginning of the rail so that it arrives to the position with the
minimal speed.

Juan has observed that for each centimetre that the carriages go up,
those ones loose A mm/s of speed for the gravity, while that for each
centimetre that they go down, those ones win A mm/s of speed. Moreover,
for each metre of covered track, caused by the friction of the track,
those ones loose B mm/s of speed. Juan wants that the carriage stops in
the position indicated by Maria, that is in a distance of X cm in
horizontal from the beginning of the rail. Juan wants to know the
minimal speed he has to launch the carriage with in order to it arrives
to the point indicated by Maria.

Input

The input will consist of various test data. The first line will contain
a number that will indicate the number of test data to solve. Each test
data will start with 4 numbers A, B, X and N, in this order, in a line,
where N will be the number of stretches of the track and will be
integer. The following N + 1 lines will contain N + 1 pairs of points
(x_(i), y_(i)) with x_(i) and y_(i) measured in milimitres and being
integers, where (0, 0) will be the first point and x_(i) will be stricly
increasing, that is, x_(i) < x_(i + 1). These points represent a track
of N straight stretches joined. It is known that N ≤ 1000 and that
|y_(i)| ≤ 100.

Output

For each case, your program must print in a line the ceiling of the
minimal speed in mm/s that the carriage must be launched with to reach
the point indicated by Maria.

Pista: Consider that, the faster you launch the carriage from the
origen, the farther it will arrive. Therefore, it can be known that if
the carriage does not reach the position P with a determinated speed, it
must be launched with more speed.

Author: Ricardo Martín

The solution can be found iterating though the track until arriving to
the position X.

PROBLEMAS DOUBLE En caso de llegar a un pico con velocidad 0, como
decidimos si sigue hacia abajo o no?? Solucion = no puede haber picos...
si os parece..

Problem information

Author: Unknown
Translator: Carlos Molina

Generation: 2026-01-25T11:05:09.551Z

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