As an employee of Aqueous Contaminate Management, you must
monitor the pollution that gets dumped (sometimes accidentally,
sometimes purposefully) into rivers, lakes and oceans. One of
your jobs is to measure the impact of the pollution on various
ecosystems in the water such as coral reefs, spawning grounds,
and so on.
The model you use in your analysis is illustrated in
Figure 1. The shoreline (the horizontal line in the
figure) lies on the $x$axis with the source of the
pollution located at the origin (0,0). The spread of the
pollution into the water is represented by the semicircle, and
the polygon represents the ecosystem of concern. You must
determine the area of the ecosystem that is contaminated,
represented by the dark blue region in the figure.
Input
The input consists of a single test case. A test case starts
with a line containing two integers $n$ and $r$, where $3 \le n \le 100$ is the number of
vertices in the polygon and $1
\le r \le 1\, 000$ is the radius of the pollution field.
This is followed by $n$
lines, each containing two integers $x_ i, y_ i$, giving the coordinates
of the polygon vertices in counterclockwise order, where
$1\, 500 \le x_ i \le 1\,
500$ and $0 \le y_ i \le
1\, 500$. The polygon does not selfintersect or touch
itself. No vertex lies on the circle boundary.
Output
Display the area of the polygon that falls within the
semicircle centered at the origin with radius $r$. Give the result with an absolute
error of at most $10^{3}$.
Sample Input 1 
Sample Output 1 
6 10
8 2
8 2
8 14
0 14
0 6
8 14

101.576437872
