You got a new guard offer yesterday. Now you are at the company, and your boss asks you to stand at somewhere to do your job -- guard.
You can treat the building as a simple polygon, and your job is finding a position to make sure that you can see the largest area. Please notice that, you have a range of vision, that you cannot see what is out of that range. The wall of building can also block your sight.
Look at that image; if you stand at the middle then you can see the gray area.
The input consists of multiple test cases. The first line of each case contains two integers n (0 <= n <= 10) and r(0 <= r <= 100). The next n lines contain a simple polygon that consists of n points, indicating the building. The absolute value of each coordinate won’t be more than 100.
The last case is followed by a line containing two zeros which should not be processed.
Output the largest area that you can see. Please take it with two fractional digits and make sure that your program won’t output “-0.00”.