“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?
输入解释
The first line contains T (1 ≤ T ≤ 1000), the count of testcases.
Then the next T lines, each of them contains two integer a and b (1 ≤ a,b ≤ 1000).
输出解释
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 $\frac{|a-b|}{max\{1,|b|\}}$ ≤ $10^{-4}$, where max{x,y} means the maximum of x and y and |x| means the absolute value of x.
输入样例
2
3 4
1000 1000
输出样例
76.27433388
7141592.65358979
提示
August sipped away like a bottle of wine.
This is the rendered picture for the example.