Points on a Circle

You place $n$ points at random on the circumference of a circle of radius 1. Each point is equally likely to land anywhere on the circumference.

Let $P$ be the probability that all $n$ points lie on one arc of that same circle whose central angle is at most $p$ degrees. The arc may begin at any point of the circumference.

Because $P$ can be extremely small, print $-\log_2 P$ instead of $P$.

The first line contains the number of points $n$ and the angle $p$. ($1 \le n \le 100000$, $1 \le p < 180$)

Both $n$ and $p$ are positive integers.

Print $-\log_2 P$ with exactly six digits after the decimal point, rounded at the seventh digit.