A qanat is an irrigation system widely used to
deliver water in hot, arid climates. The technology was
originally developed by Persians over 2000 years ago. In
Morocco, qanats are known as khettara and are still used today
in the southern part of the country.
The basic feature of a qanat is an essentially horizontal
channel that brings water from an underground water source to
an outlet near a civilization. There is also a shaft known as a
mother well that rises vertically from the underground
water source to the surface of a mountain or hill. Creating
such a system is extremely expensive, and was especially so in
ancient times, since all of the materials excavated from the
channel and mother well must be carried above ground, either
through the channel outlet or the top of the mother well. To
aid in the construction, there are often one or more additional
vertical shafts placed at strategic locations above the
underground channel. Although these shafts must also be
excavated, they provide a means for lifting additional dirt
from the horizontal channel as illustrated in Figure 1.
For this problem, model the crosssection of a qanat as
shown in Figure 2, with the channel outlet at $(0,0)$, the water source at
$(w,0)$, and the top of
the mother well at $(w,h)$
with $w > h$. The
surface of the mountain extends along a straight line from
$(w,h)$ to $(0,0)$.
Every qanat must have a vertical mother well from the water
source to the mountain surface above, along with $n$ additional vertical shafts. The
channel and all shafts are modeled as line segments. Your goal
is to determine the placement for those additional shafts so as
to minimize the overall excavation cost. This cost is equal to
the sum of the distances that each piece of excavated dirt must
be transported to reach the surface (using any combination of
horizontal and vertical movement). For example, the cost of
excavating a continuous section of dirt starting from the
surface and going along a path of length $\ell $ (possibly including turns) is
$\int _0^{\ell } x \, dx =
\frac{1}{2} \ell ^2$.
Input
The input consists of a single line containing three
integers $w$ ($1 \le w \le 10\, 000$), $h$ ($1
\le h < w$), and $n$ ($1 \le n \le 1\, 000$). The value
$w$ is the horizontal
distance from the water source to the qanat outlet. The value
$h$ is the vertical
distance from the water source to the mountain surface. The
value $n$ is the number of
vertical shafts that must be used in addition to the mother
well.
Output
First, display the minimum overall excavation cost. Next,
display the $x$coordinates, in increasing order,
for $n$ optimally placed
vertical shafts. If $n >
10$, display only the first $10$ $x$coordinates. Answers within an
absolute or relative error of $10^{4}$ will be accepted. You may
assume that there is a unique solution. No test case will
result in a shaft within $0.001$ units from the outlet of the
qanat channel or from another shaft.
Sample Input 1 
Sample Output 1 
8 4 1

31.500000
3.000000

Sample Input 2 
Sample Output 2 
195 65 2

12220.000000
48.000000
108.000000

Sample Input 3 
Sample Output 3 
10000 1 1000

30141.885677
9.956721
19.913443
29.870164
39.826887
49.783610
59.740334
69.697060
79.653786
89.610515
99.567245
