Problem D
Cheetah
Input: standard input
Output: standard output
Time Limit: 1 second

The cheetah is a beautiful hunting animal. Although it can gain incredible speed, it tires soon and so cannot maintain the speed for long. So in an attempt to catch a prey, the cheetah must choose a path of minimum length.

The cheetah quietly and discreetly closes in on the prey. When the cheetah is at position (Cx, Cy) and the prey at position (Px, Py), the prey realizes that the cheetah is close by and starts running with the constant speed of U feet per second at an angle P with the positive direction of X-axis. The cheetah also starts running at a constant speed of V feet per second at an angle C to ensure that he can catch the prey with minimum effort. The cheetah, however, cannot maintain the speed for more than L seconds.

Provided the values of Cx, Cy, Px, Py, P, U, V, L, you have to find C, T, X, Y, where T is the time required for the cheetah to catch the prey and (X,Y) is the position at which the cheetah catches the prey.
The co-ordinates are in feet and range between [0, 10000]. The angles are in degrees and range between [0, 360]. The velocities range between [0, 500]. L ranges between [0, 10000].

Input

The first line gives the number of test cases.

Each of the test case consists of a line containing 8 integers giving the values of Cx, Cy, Px, Py, P, U, V, L in that order.

 

Output

For each test case, if the cheetah can catch the prey, then print the values of C, T, X, Y in that order. Each value should have 2-digits after the decimal point. If the cheetah cannot catch the prey within L seconds, then print "sorry, buddy".

Sample Input                                Output for Sample Input   

2
0 0 6 0 135 1 1 10
0 0 6 0 135 1 1 3
 
 
45.00 4.24 3.00 3.00
sorry, buddy
 

 

Problem setter: Sadrul Habib Chowdhury                                                  

Special Thanks: Derek Kisman, EPS.