P6376 [PA 2010] The Goat

There are $n$ points on a plane. Repeat the following operation $k$ times: randomly choose one point, and draw a circle with radius $r$ centered at that point. Find the expected area of the union of all circles in the end.

The first line contains three integers $n, k, r$. The next $n$ lines each contain two integers $x, y$, representing a point.

Output the expected area of the union. An error within $10^{-2}$ is accepted.

#### Constraints For all testdata, it is guaranteed that $1 \le n, k \le 10^3$, $1 \le r \le 10^3$, and $|x|, |y| \le 10^3$. Translated by ChatGPT 5