Billiard

A rectangular billiard table has a horizontal side of $a$ inches and a vertical side of $b$ inches. A ball is launched from the exact center of the table. After $s > 0$ seconds the ball returns exactly to the point from which it was launched, having bounced $m$ times off the vertical sides and $n$ times off the horizontal sides.

Find the launching angle $A$ (measured from the horizontal, always between 0 and 90 degrees inclusive) and the initial speed of the ball.

Assume that every collision with a side is perfectly elastic (no energy loss), so the velocity component parallel to that side is unchanged by the bounce. Assume the ball has zero radius. Unlike an ordinary pool table, this billiard table has no pockets.

The input consists of several lines. Each line contains five positive integers $a$, $b$, $s$, $m$, and $n$, in that order, separated by whitespace. Every value is a positive integer no greater than 10000.

The last line contains five zeroes; it marks the end of the input and is not processed.

For each input line except the last (0 0 0 0 0), print one line containing two real numbers separated by a single space, each rounded to exactly two decimal places. The first number is the angle $A$ in degrees, and the second is the ball's initial speed in inches per second.