Clearing Space

You are putting up an event space in Nottingham's Sherwood Forest by erecting
a fence in a circular-shaped clearing you found that is exactly one kilometre in
radius. You will put some fence posts in the trees around the edge of the
clearing and then connect them together with fencing later.

You would like to put the fence around as much of the event space as possible.
However, the ground is only suitable in a few places around the border, and you
only have so many fence posts to put in the ground, so you'll have to choose
carefully if you want to maximise area.

figure[!h]
sample1.pdf
An illustration of using 4 posts to capture the maximum area in sample input 1.
figure

Knowing the safe places to put fence posts, and the number of posts you have,
what is the maximum area of clearing you can enclose?

Input
	itemize
    One line containing the integer number of safe points around the
          km-radius clearing,  ().
    One line containing the integer number of fence posts you have,
           ().
    One line containing  distinct real numbers  in ascending order,
          the angles in degrees of each of the safe places to add fence posts ().
	itemize

Output
  Output the maximum area you can capture with a polygonal clearing made using
  at most  fence posts, in square metres.

  The output must be accurate to an absolute or relative error of .

  As a reminder, the radius of the clearing is km.
