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### Problem

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

### Example

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 about 142.8571429 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 p seconds after the game starts you'll have 2p cookies.

### Input

The first line of the input gives the number of test cases, T. T lines follow. Each line contains three space-separated real-valued numbers: C, F and X, 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.

### Output

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.

We recommend outputting y to 7 decimal places, but it is not required. y will be considered correct if it is close enough to the correct number: within an absolute or relative error of 10-6. See the FAQ for an explanation of what that means, and what formats of real numbers we accept.

### Limits

1 <= T <= 100.

1 <= C <= 10000.
1 <= F <= 100.
1 <= X <= 100000.

### Sample

 Input `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` Output `Case #1: 1.0000000``Case #2: 39.1666667``Case #3: 63.9680013``Case #4: 526.1904762`

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