Ball in a Rectangle 

Input: Standard Input Output: Standard Output

  There is a rectangle on the cartesian plane, with bottom-left corner at (0,0) and top-right corner at (L, W). There is a ball centered at (x, y), with radius=R, shown below

At time 0, the ball starts to move along a ray with polar angle a (the angle from positive x-axis to the ray, rotating counter-clockwise). When hitting the rectangle boundary, the reflex angle always equals to the incidence angle. The ball's velocity is always v (i.e. it never changes when hitting the rectangle). Where is the center of the ball at time s?

Input 

There will be at most 25 test cases, each contains a line with 8 integers L,W,x,y,R,a,v,s (100$\le$L,W$\le$109, 1$\le$R$\le$5, R$\le$x$\le$L - R, R$\le$y$\le$W - R, 0$\le$a < 360, 1$\le$v, s$\le$109), as stated above. The input terminates with L = W = x = y = R = a = v = s = 0, which should not be processed.

Output 

For each test case, output a line containing two floating-point numbers x, y, rounded to two decimal points, indicating that the center of ball will be at (x, y) at time s.

Sample Input 

100 100 80 10 5 90 2 23
110 100 70 10 5 180 1 9999
0 0 0 0 0 0 0 0

Sample Output 

80.00 56.00
71.00 10.00

Problemsetter: Rujia Liu, Special Thanks: Yiming Li, Shamim Hafiz & Sohel Hafiz