Pie

My birthday is coming up, and by tradition I serve pie. Not just one pie — I have $N$ of them, of various tastes and sizes. $F$ friends are coming to the party, and each of them gets one piece of pie. To keep things tidy this must be a single piece cut from one pie, not several small pieces, though a whole pie may count as one piece.

My friends are picky: if anyone gets a bigger piece than the others, they start complaining. So everyone must get an equally sized piece (the shapes may differ), even if this means some pie is wasted. Of course I want a piece for myself too, and it must be the same size.

Every pie is a cylinder of the same height $1$, but the radii $r_i$ may differ. What is the largest volume of piece that I and all of my friends can each get?

The first line contains a positive integer: the number of test cases. Then, for each test case:

• One line with two integers $N$ and $F$ ($1 \le N, F \le 10000$): the number of pies and the number of friends.
• One line with $N$ integers $r_i$ ($1 \le r_i \le 10000$): the radii of the pies.

For each test case, output on one line the largest volume $V$ such that I and all of my friends can each get a piece of size $V$, rounded to exactly four decimal places. (The original problem allows any real number within an absolute error of $10^{-3}$; for automatic judging the answer is printed with a fixed four-decimal format.)