Description

Original Source: ZOJ 3203

Compared to wildleopard's home, his younger brother mildleopard is relatively poor. His house is narrow, and there is only one light bulb in his room. Every night, he wanders around his cramped house, pondering how to earn more money. One day, he noticed that the length of his shadow changes as he walks between the light bulb and the wall. A sudden idea struck him—he wanted to determine the maximum length his shadow could reach.

Input Format

The first line of the input file contains an integer $T$, representing the number of test cases.

For each test case, there is only one line containing three real numbers $H$, $h$, and $D$. Here, $H$ denotes the height of the light bulb, $h$ represents mildleopard's height, and $D$ is the horizontal distance between the light bulb and the wall.

Output Format

The output file should consist of $T$ lines, one for each test case, indicating the maximum length of the shadow, rounded to three decimal places.

Sample 1

3
2 1 0.5
2 0.5 3
4 3 4

1.000
0.750
4.000

Constraints & Hints

$T \leq 100$, $10^{-2} \leq H, h, D \leq 10^3$, $10^{-2} \leq H - h$.