Having stayed in the forest his whole life, Shroomish wants to go out and explore the world! Unfortunately, having not evolved a protective hat yet, Shroomish is very afraid of sunlight. You decide to help by making a pair of sunglasses for Shroomish. Unfortunately, Shroomish is quite particular about how these sunglasses should look. Specifically, each of the 2 lenses must be in the shape of an equilateral triangle. Shroomish also demands that each of these lenses have sidelengths $$$a$$$ and $$$b$$$ respectively.
Unfortunately, the only lens store in town sell lenses which are perfect circles, so you need to buy a circular lens and cut out the triangular lenses yourself. While you are able to make cuts, you do not have the tools to merge two pieces together.
Having explained yourself to the store owner, she explains that they have a variety of lens sizes; you are able to buy a circular lens with radius $$$r$$$, for any positive real number $$$r$$$. However, she expresses disdain at the idea of cutting the lenses, and only allows you to buy one lens. Additionally, she dislikes wasting resources, and will only sell you a lens if it is the smallest lens you need to complete your task. Even worse, she wants you to calculate the size of the lens you need to buy!
Given all these requirements, what is the radius of the lens you need to buy to craft the lenses needed to make Shroomish a pair of sunglasses?
The only line of each test case contains two integers $$$a$$$ and $$$b$$$, the sidelengths of the two triangles respectively $$$(1 \leq a, b \leq 10^6)$$$.
Output a single number, the radius of the lens you will buy. Your answer will be accepted if it is within an absolute or relative error of $$$10^{-6}$$$ to the Jury's answer.
Remember to print floating-point numbers with enough precision! This can be done explicitly with f-strings in Python, or with setprecision() in C++.
1 1
0.8660254038
69 420
242.4871130596
1000 2727
1613.8383399523
In test case 1, an optimal arrangement could look like this:
In test case 2, an optimal arrangement could look like this:
In test case 3, an optimal arrangement could look like this:
