CF681E Runaway to a Shadow

Dima is living in a dormitory, as well as some cockroaches. At the moment $ 0 $ Dima saw a cockroach running on a table and decided to kill it. Dima needs exactly $ T $ seconds for aiming, and after that he will precisely strike the cockroach and finish it. To survive the cockroach has to run into a shadow, cast by round plates standing on the table, in $ T $ seconds. Shadow casted by any of the plates has the shape of a circle. Shadow circles may intersect, nest or overlap arbitrarily. The cockroach uses the following strategy: first he equiprobably picks a direction to run towards and then runs towards it with the constant speed $ v $ . If at some moment $ t

In the first line of the input the four integers $ x_{0} $ , $ y_{0} $ , $ v $ , $ T $ ( $ |x_{0}|,|y_{0}|

Print the only real number $ p $ — the probability of that the cockroach will stay alive. Your answer will be considered correct if its absolute or relative error does not exceed $ 10^{-4} $ .

The picture for the first sample is given below. Red color stands for points which being chosen as the cockroach's running direction will cause him being killed, green color for those standing for survival directions. Please note that despite containing a circle centered in $ (-2,2) $ a part of zone is colored red because the cockroach is not able to reach it in one second.