"Remember when I pulled up and said get in the car, and then cancelled my plans just in case you'd call, back when I was living for the hope of it all."
After death by a thousand cuts, he found his love. He has two parameter $$$a$$$ and $$$b$$$, and he wants to show his lover a piece of drawing bounded by the following math curves.
$$$$$$ \begin{cases} y = \sqrt{a^2 - (x-a)^2} \\ y = \sqrt{a^2 - (x+a)^2} \\ y = \frac{2b}{\pi} \left( \arccos \left(\frac{x+a}{a}\right) - \pi \right) \\ y = \frac{2b}{\pi} \left( \arcsin \left(\frac{x-a}{a}\right) - \frac{\pi}{2} \right) \end{cases} $$$$$$
Now his lover wants to know the area bounded by the close curve. Can you tell him?
The first line contains $$$T ~ (1 \le T \le 1000)$$$, the count of testcases.
Then the next $$$T$$$ lines, each of them contains two integer $$$a$$$ and $$$b ~ (1 \leq a, b \leq 1000)$$$.
For each test case, output a number for the answer with an absolute or relative error of at most $$$10^{-4}$$$. Precisely speaking, assume that your answer is $$$a$$$ and and the jury's answer is $$$b$$$, your answer will be considered correct if $$$\frac{|a-b|}{max\lbrace 1, |b|\rbrace} \le 10^{-4}$$$, where $$$\max\lbrace x,y\rbrace$$$ means the maximum of $$$x$$$ and $$$y$$$ and $$$|x|$$$ means the absolute value of $$$x$$$.
2 3 4 1000 1000
76.27433388 7141592.65358979
August sipped away like a bottle of wine.
This is the rendered picture for the example.
