Problem D
Wonky Pizza

Illustration of Sample Input 1. The first cut at $\theta =0$ is along the solid blue line, and the second cut at $\theta \approx 3.74633$ is along the dashed blue line. Together, the cuts split the pizza into two pieces of equal area.

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 doesn’t exceed $10^{-4}$.

0.5 1 2

3.746330709824588

3 2 5

2.4186792326212
3.766428671586681
4.767487090895717
5.584103675011194