시간 제한메모리 제한제출정답맞힌 사람정답 비율
10 초 64 MB0000.000%

## 문제

Once you have X cookies that you haven't spent on farms, you win! Write a program to figure out how long it will take you to win if you use the best possible strategy.

Suppose C=500.0, F=4.0 and X=2000.0. Here's how the best possible strategy plays out:

2. After 250 seconds, you will have C=500 cookies and can buy a farm that produces F=4 cookies per second.
6. Another farm will cost 500 cookies, which you can buy after 50 seconds.
8. Another farm would cost 500 cookies, but it actually makes sense not to buy it: instead you can just wait until you have X=2000 cookies, which takes about142.8571429 seconds.

Total time: 250 + 83.3333333 + 50 + 142.8571429 = 526.1904762 seconds.

Notice that you get cookies continuously: so 0.1 seconds after the game starts you'll have 0.2 cookies, and π seconds after the game starts you'll have 2π cookies.

## 입력

The first line of the input gives the number of test cases, T (1 <= T <= 100). T lines follow. Each line contains three space-separated real-valued numbers: C (1 <= C <= 500), F (1 <= F <= 4 and X (1 <= X <= 2000), whose meanings are described earlier in the problem statement.

C, F and X will each consist of at least 1 digit followed by 1 decimal point followed by from 1 to 5 digits. There will be no leading zeroes.

## 출력

For each test case, output one line containing "Case #x: y", where x is the test case number (starting from 1) and y is the minimum number of seconds it takes before you can have X delicious cookies. The output must be real numbers with 4-digit decimal fraction.

## 예제 입력 1

4
30.0 1.0 2.0
30.0 2.0 100.0
30.50000 3.14159 1999.19990
500.0 4.0 2000.0


## 예제 출력 1

Case #1: 1.0000
Case #2: 39.1667
Case #3: 63.9680
Case #4: 526.1905