SP390 BILLIARD - 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 description above.