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 $10\, 000$.
Input is terminated by a line containing five zeroes.
Output
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
