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..

Information

- Author
- Omer Giménez
- Language
- English
- Translator
- Carlos Molina
- Original language
- Spanish
- Other languages
- Spanish
- Official solutions
- C++
- User solutions
- C++