BILLIARD  Billiard
In a billiard table with horizontal side a inches and vertical side b inches, a ball is launched from the middle of the table. After s > 0 seconds the ball returns to the point from which it was launched, after having made m bounces off the vertical sides and n bounces off the horizontal sides of the table. Find the launching angle A (measured from the horizontal), which will be between 0 and 90 degrees inclusive, and the initial velocity of the ball.
Assume that the collisions with a side are elastic (no energy loss), and thus the velocity component of the ball parallel to each side remains unchanged. Also, assume the ball has a radius of zero. Remember that, unlike pool tables, billiard tables have no pockets.
Input
Input consists of a sequence of lines, each containing five nonnegative integers separated by whitespace. The five numbers are: a, b, s, m, and n, respectively. All numbers are positive integers not greater than 10000.
Input is terminated by a line containing five zeroes.
Output
For each input line except the last, output a line containing two real numbers (accurate to two decimal places) separated by a single space. The first number is the measure of the angle A in degrees and the second is the velocity of the ball measured in inches per second, according to the description above.
Example
Input: 100 100 1 1 1 200 100 5 3 4 201 132 48 1900 156 0 0 0 0 0 Output: 45.00 141.42 33.69 144.22 3.09 7967.81
hide comments
Fish3R:
20120728 07:19:12
@Sandeep Singh Jakhar


ɥsǝןǝǝu:
20120727 18:49:36
i got wrong answer with float but accepted by changing it to double.... 

Adrian Kuegel:
20120611 10:33:51
@sanctity: sorry, but the problem tells you exactly what you should print. If you don't do it, its your fault. 

NOODLES:
20120521 16:44:07
WTF.......a new line feed costed me 5 wrong answers.....idiotic....


NOODLES:
20120521 15:18:31
are there any tricky cases.......i have checked my o/p is correctfor all possible cases but still getting a WA :( somebody help plzzzzzzzzzzzzzzzz 

Sandeep Singh Jakhar:
20120515 14:58:13
i'm getting incorrect o/p for 3rd testcase..help..:P 

Parth Tripathi:
20120106 08:23:22
more test cases please


Aquid Shahwar:
20111217 18:39:47
my all the ans are comng correct,then also it is giving wa,,can anyone help me. 

Alejandro Hitti:
20110323 14:00:33
Took me a while to get this one... It was easy after I realized the ball doesn't stop when it gets to the middle again, it just goes by :p Last edit: 20110323 17:10:15 

Efim:
20100718 17:44:12
are numbers nonnegative or positive? 
Added by:  Adrian Kuegel 
Date:  20050704 
Time limit:  0.572s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  University of Waterloo Local Contest (Spring 1999) 