Problem N
Amsterdam Distance
Languages
en
ja
Your friend from Manhattan is visiting you in Amsterdam.
Because she can only stay for a short while, she wants to see
as many tourist attractions in Amsterdam in as little time as
possible. To do that, she needs to be able to figure out how
long it takes her to walk from one landmark to another. In her
hometown, that is easy: to walk from point
since Manhattan looks like a rectangular grid of city blocks. However, Amsterdam is not well approximated by a rectangular grid. Therefore, you have taken it upon yourself to figure out the shortest distances between attractions in Amsterdam. With its canals, Amsterdam looks much more like a half-disc, with streets radiating at regular angles from the center, and with canals running the arc of the circle at equally spaced intervals. A street corner is given by the intersection of a circular canal and a street which radiates from the city center.
Depending on how accurately you want to model the street plan of Amsterdam, you can split the city into more or fewer half rings, and into more or fewer segments. Also, to avoid conversion problems, you want your program to work with any unit, given as the radius of the half circle. Can you help your friend by writing a program which computes the distance between any two street corners in Amsterdam, for a particular approximation?
Input
The input consists of
-
One line with two integers
and a real number .-
is the number of segments (or ‘pie slices’) the model of the city is split into. -
is the number of half rings the model of the city is split into. -
is the radius of the city, given with at most digits after the decimal point.
-
-
One line with four integers,
, with , and , the coordinates of two corners in the model of Amsterdam.
Output
Output a single line containing a single real number, the
least distance needed to travel from point
Sample Input 1 | Sample Output 1 |
---|---|
6 5 2.0 1 3 4 2 |
1.65663706143592 |
Sample Input 2 | Sample Output 2 |
---|---|
9 7 3.0 1 5 9 5 |
4.28571428571429 |
Sample Input 3 | Sample Output 3 |
---|---|
10 10 1.0 2 0 6 0 |
0 |