F. Pull
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

In the game Arknights, you can cost materials to headhunt an operator, which is known as a pull. Initially, the 6-star operators' rate is $$$a\%$$$. In other words, the probability that you obtain a 6-star operator is $$$a\%$$$. If a 6-star operator does not appear after $$$c$$$ pulls, each subsequent pull will increase the 6-star operators' rate by $$$b\%$$$, up to $$$100\%$$$. For example, on the $$$(c+1)$$$-th pull, the rate increases to $$$(a+b)\%$$$, and then on the $$$(c+2)$$$-th pull, the rate increases to $$$(a+2b)\%$$$. The pull count and increased rate will be reset as soon as a 6-star operator appears on any pull.

Given $$$a$$$, $$$b$$$, and $$$c$$$, find the expected pulls between two 6-star operators. In other words, if you have just obtained a 6-star operator, find the expected pulls that you need to obtain a next 6-star operator.

Input

Each test contains multiple tests. The first line contains one integer $$$t$$$ ($$$1\le t\le 10^3$$$) — the number of test cases. The description of each test case follows.

The only line of each test case contains three integers $$$a$$$, $$$b$$$, and $$$c$$$ ($$$1\le a,b,c\le 100$$$).

Output

For each test case, output one real number — the expected pulls between two consecutive 6-star operators.

Your answer is considered correct if its absolute or relative error does not exceed $$$10^{-6}$$$. Formally, let your answer be $$$a$$$, and the jury's answer be $$$b$$$. Your answer is accepted if and only if $$$\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-6}$$$.

Example
Input
3
1 1 1
2 2 50
100 100 100
Output
12.20996063021597
34.59455493520978
1.00000000000000