Mr. Arnold Gerald Nostik is in charge of the design of the main rose window
of the new cathedral in his town.
The rose window is circular, 2*r* units wide.
Since Mr. A. G. Nostik knows little about Virgins, Saints and Angels,
he is thinking about a geometric pattern.
Let *n* be an even integer number, at least 4.
Mr. Nostik plans to pick *n* points,
each at distance *r* of the center of the window,
these points being the vertices of a regular polygon.
(The next page shows an example with *n* = 8.)
These points are to be joined with straight lines,
and the resulting regions colored
(with arbitrary colors) as shown in the example.
Note that for *n* = 8 there are four regions.
We number these regions 1, 2, 3 and 4
starting to count from the center of the rose.
In general, there are *n*/2 regions.

Write a program to help Mr. Nostik to know how much glass of every color he needs in order to build a given rose window.

**Input**

Input begins with a number *t*.
Follow *t* cases, each with a real number *r*,
an even integer number *n*, and an integer number *k*.
Assume 1 ≤ *r* ≤ 100, 4 ≤ *n* ≤ 40, and 1 ≤ *k* ≤ *n*/2.

**Output**

For every case,
print the area of the *k*-th region of a rose window
with *n* points and radius *r*,
with four digits after the decimal point.
The input cases have no precision issues.

Public test cases

**Input**

4 50 8 3 9.238794 8 2 10 4 1 20 4 1

**Output**

2928.9322 100.0000 200.0000 800.0000

Information

- Author
- Salvador Roura
- Language
- English
- Official solutions
- C++
- User solutions
- C++
- Event
- Segon Concurs de Programació de la UPC - Final
- Date
- 2004-09-29