Expected Union Area of Circles

There are $n$ points on a plane. We repeat the following operation $k$ times: randomly select one of the points uniformly and draw a circle centered at that point with radius $r$. Assuming that circles drawn from different points do not overlap, the expected union area of the circles is given by

$$E = \pi r^2 \cdot \left(n \left(1 - \left(1-\frac{1}{n}\right)^k\right)\right). $$

Compute and output this expected area.

inputFormat

The input consists of a single line containing three numbers: $n$, $r$, and $k$. Here, $n$ ($1\le n\le10^9$) is the number of points, $r$ ($r>0$) is the radius of the circle, and $k$ ($k\ge0$) is the number of operations.

outputFormat

Output the expected union area of the circles. Answers within an absolute or relative error of $10^{-6}$ will be accepted.

sample

5 1.0 3

7.667912