Dima and the Computer Game
Dima is playing a computer game where, on one level, he drives a car that must navigate a road with a 90° turn.
This section of the road is composed of two roads intersecting at a right angle, as depicted in the figure:
The car can move either in a straight line or along a circular arc, with its direction changing continuously.
Your task is to determine the path from a point far to the left to a point far below on the road. Define the turning radius of the path as the smallest radius among all the circular arcs on this path. What is the largest turning radius that allows Dima to navigate this section of the road?
Input
The input consists of a single line with two integers w_1 and w_2 (1 ≤ w_1, w_2 ≤ 100) — representing the widths of the left and bottom parts of the road, respectively.
Output
Output a single number — the maximum turning radius. The answer will be considered correct if its relative error does not exceed 1e-9.