TDMU #5 Chicken Leg

#### Start

2019-01-03 06:00 UTC

## TDMU #5 Chicken Leg

#### End

2019-01-10 06:00 UTC
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# Problem BOrnaments

A factory is making ornaments for the upcoming holidays. Ornaments consist of a 2D glass sphere (i.e., a circle) that is designed to hang off a hook or nail using a string that tightly wraps around the ornament, as shown in the figure to the right.

Your task is to write a program that calculates the length of the string, given the radius $r$ of the circle, the distance $h$ from the knot to the center of the circle, and some multiplier to account for the excess needed to tie the knot.

## Input

The input will contain multiple test cases, up to $200$. Each test case contains on a single line three integers $r$ ($1 \le r \le 10,000$), $h$ ($r \le h \le 10,000$), and $s$ ($0 \le s \le 100$). $s$ denotes the necessary excess string in %. The percentage is relative to what would be needed without accounting for the knot, so if $s = 25$, you should increment the necessary length by $1/4$.

The input will be terminated by a line containing $3$ zeros.

## Output

For each test case, output the length of the needed string, rounded to two decimals.

Sample Input 1 Sample Output 1
1 3 10
2 5 8
10 11 0
0 0 0

10.43
18.46
63.40