Tom and Jerry

Tom and Jerry are very fond of cat and mice games, which might be rather obvious to you. Today they

are playing a very complicated game. The goals are simple as usual though, Jerry would be running

and Tom would have to catch Jerry.

However, today Jerry is running on a perfect circular

path with radius R meters, at a constant speed of

V m/s. Initially Tom is sitting at the very center of

the circle. He wants to catch Jerry as soon as possible,

but we all know, Tom is not very intelligent. Instead

of calculating an optimal direction to catch Jerry, he is

just running towards Jerry.

As Jerry is also moving, the path Tom has taken

start to look like a curve (see picture above). At any

given moment, Tom’s position is between Jerry’s current                

position and the center of the circle. Tom is also

moving at a constant speed of V m/s, same speed as

Jerry. Find the time (in seconds) Tom would need to

catch Jerry.

Input

Input file has T (T ≤ 10000) test cases, each case consists of two integer R and V . Here, 0 < R, V ≤

10000.

Output

For each test case, print the case number and the time Tom will need to catch Jerry. Floating point

rounding error lower than 10−5 will be ignored by the judge.

Sample Input

4

45 100

5 1547

1000 10000

5668 5467

Sample Output

Case 1: 0.70685835

Case 2: 0.00507691

Case 3: 0.15707963
Case 4: 1.62854830



题意:

     圆，半径为R，Jerry以速度V在圆周上移动，Tom在圆心以同样的速度始终面向Jerry跑去，即在任意时刻，Tom，Jerry，圆心总在同一直线，问Tom追到Jerry所需时间

思路：

     几何问题，Tom一直面向Jerry跑去，可推出当Tom追到Jerry时，Jerry走过了半径为R的1/4圆周，Tom走了半径为R/2的1/2圆周，那么时间等于2*PI*R/4/V