Rabbits and Polygons. HARD#3267
rabbits are positioned at the vertices of a regular -gon with side length . They all start moving simultaneously at a constant speed . The first rabbit moves towards the second, the second towards the third, the third towards the fourth, and so on, with the -th rabbit moving towards the first. After a certain time , all rabbits will converge at a single point. Each rabbit wants to know the distance it will travel before this meeting occurs. Help them determine this distance.
Each test case consists of numbers: a natural number (1 \le N < 2^{20}), a real number (0 < a < 2^{20}), and a real number (0 \le v < 2^{20}).
Output the distance one rabbit will travel until the meeting, with an absolute error of 10^{-9}, or output if the rabbits will never meet.
Example 1