2017-09-13 00:00 CEST

PSU Meeting 1


2017-09-20 00:00 CEST
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Problem B

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 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 $10\, 000$.

Input is terminated by a line containing five zeroes.


For each input line except the last, output a line containing two real numbers (rounded to exactly 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.

Sample Input 1 Sample Output 1
100 100 1 1 1
200 100 5 3 4
201 132 48 1900 156
0 0 0 0 0
45.00 141.42
33.69 144.22
3.09 7967.81