The queen wishes to build a patio paved with of a circular
center stone surrounded by circular rings of circular stones.
All the stones in a ring will be the same size with the same
number of stones in each ring. The stones in the innermost ring
will be placed touching (tangent to) the adjacent stones in the
ring and the central stone. The stones in the other rings will
touch the two adjacent stones in the next inner ring and their
neighbors in the same ring. The figures below depict a patio
with one ring of three stones and a patio with 5 rings of 11
stones. The patio is to be surrounded by a fence that goes
around the outermost stones and straight between them (the
heavier line in the figures).
The queen does not yet know how many stones there will be in
each circle nor how many circles of stones there will be. To be
prepared for whatever she decides, write a program to calculate
the sizes of the stones in each circle and the length of the
surrounding fence. The radius of the central stone is to be one
The first line of input contains a single integer
$P$, ($1 \le P \le 200$) which is the number
of data sets that follow. Each data set should be processed
identically and independently.
Each data set consists of a single line of input. It
contains the data set number, $K$, the number, $N$ ($3
\le N \le 20$), of stones in each circle and the number,
$M$ ($1 \le M \le 15$), of circles of
stones around the central stone.
For each data set there is a single line of output. It
contains the data set number, $K$, followed by a single space which
is then followed by the radius (in queenly feet) of the stones
in the outermost ring (to $3$ decimal places) which is followed
by a single space which is then followed by the length (in
queenly feet) of the fence (to $3$ decimal places).
|Sample Input 1
||Sample Output 1
1 3 1
2 7 3
3 11 5
1 6.464 79.400
2 3.834 77.760
3 2.916 82.481