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F - Regular Triangle Inside a Rectangle

Score : $500$ points

Problem Statement

Find the maximum side length of a regular triangle that can be drawn within a rectangle whose side lengths are $A$ and $B$.

Constraints

• $1 \leq A,B \leq 1000$
• $A$ and $B$ are integers.

Input

The input is given from Standard Input in the following format:

$A$ $B$

Output

Print the answer.
Your output is considered correct if the absolute or relative error from the true answer is at most $10^{-9}$.

1 1

1.03527618041008295791

The following figure shows an optimal drawing, with the side length of $\sqrt{6} - \sqrt{2}$.

Note that the sample output does not strictly match $\sqrt{6}- \sqrt{2}$, but the error is within $10^{-9}$, so it is considered correct.