Rose windows P91283

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, $2r$ 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 $1 \le r \le 100$, $4 \le n \le 40$, and $1 \le k \le n/2$.

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.