Highway

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 512000/512000 K (Java/Others)

Description

You just got your year-end bonus. As you had a lot of money, you decided to take your family to the United States for a twenty-day self-driving travel. One day, when you were driving on the Great Plains, you found you had left highway by accident. After checking your GPS, you realized that you were now D (0 < D <= 1000) miles from the highway. The highway is straight and extends infinitely. When you are driving outside the highway, your maximum speed is v0 mph, but on the highway you can move in a maximum speed of v1 mph (200 >= v1 > 1.2 v0 > 0). It took no time to get on or off the highway. Suddenly, it came to your mind that there was a region inside which any point can be reached within T (0 < T <= 1000) hours. You wanted to know area of this region.

Input

Input contains no more than 50 test cases.

Each test case is a single line containing 4 integers v0, v1, D and T, as above mentioned.

Output

For each test case, output your answer in a line with the case number, follow the format in sample. Its unit should be square mile. Your answer will be accepted if its absolute or relative error is less than 10-6.

This problem is special judged.

Sample Input

5 10 10 10 5 20 10 10

Sample Output

Case 1: 9360.97707377 Case 2: 14873.82733943
Hint
You should print a blank after ":" in the output.

Hint

liuyiding

Source

2014ACM/ICPC亚洲区广州站-重现赛(感谢华工和北大)

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