Kattis

# Expanding Rods

When a thin rod of length $L$ is heated $n$ degrees, it expands to a new length $L’ = (1+n \cdot C) \cdot L$, where $C$ is the coefficient of heat expansion.

When a thin rod is mounted on two solid walls and then heated, it expands and takes the shape of a circular segment, the original rod being the chord of the segment.

Your task is to compute the distance by which the center of the rod is displaced.

## Input

The input contains at most $20$ lines. Each line of input contains three non-negative numbers:

• an integer $L$, the initial lenth of the rod in millimeters ($1 \le L \le 10^9$),

• an integer $n$, the temperature change in degrees ($0 \le n \le 10^5$),

• a real number $C$, the coefficient of heat expansion of the material ($0 \le C \le 100$, at most $5$ digits after the decimal point).

The input is such that the displacement of the center of any rod is at most one half of the original rod length. The last line of input contains three $-1$’s and it should not be processed.

## Output

For each line of input, output one line with the displacement of the center of the rod in millimeters with an absolute error of at most $10^{-3}$ or a relative error of at most $10^{-9}$.

Sample Input 1 Sample Output 1
1000 100 0.0001
15000 10 0.00006
10 0 0.001
-1 -1 -1

61.328991534
225.020248568
0.000000000