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
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 |
