# Problem C

Wonky Pizza

As is customary at the ACPC, there will be pizza.^{1} However, due to logistical
challenges, the only pizza available is a wonky pizza. The
organizers will buy one wonky pizza and need to cut it into
$N$ pieces, one for each
of the $N$ contestants.
The organizers will have to fight over who gets to eat the
napkins.

A wonky pizza is like a regular pizza, except that at an angle of $\theta $ radians (measured counter-clockwise) from the positive $x$ axis, the shape extends $\frac{\alpha \theta }{2\pi }+\beta $ units from the origin, for some $\alpha $ and $\beta $ (in contrast, a normal pizza extends $r$ units from the origin at every angle $\theta $, where $r$ is the radius of the pizza).

Each cut will follow a straight line from the origin to the outer boundary, so cutting straight across the entire pizza would require two cuts. The first cut will be made at an angle of $0$ radians. Determine what angles to make the remaining $N-1$ cuts at to split the pizza into $N$ pieces of equal area.

## Input

The input consists of a single line with three numbers, $\alpha $, $\beta $, and $N$, where $0\le \alpha ,\beta \le 10$, and $N$ is an integer with $2\le N\le 100$. It is guaranteed that $\alpha $ and $\beta $ are not both zero.

## Output

The output should consist of $N-1$ lines, where the $i^{th}$ line contains the angle of cut $i$ in radians. The angles should be specified in order from smallest to largest. Your answer will be considered correct if its absolute or relative error doesnâ€™t exceed $10^{-4}$.

Sample Input 1 | Sample Output 1 |
---|---|

0.5 1 2 |
3.746330709824588 |

Sample Input 2 | Sample Output 2 |
---|---|

3 2 5 |
2.4186792326212 3.766428671586681 4.767487090895717 5.584103675011194 |

**Footnotes**

- Except in 2020 and 2021.