Problem A - 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 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.
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
100 100 1 1 1
200 100 5 3 4
201 132 48 1900 156
0 0 0 0 0