Fred and Sam are traveling together. Both have maps of the
area. The maps cover exactly the same territory, and have
exactly the same ratio of width to height, but Sam’s is at a
smaller scale than Fred’s, so it’s a bit smaller. Fred puts his
map on a table. Sam throws his map on top of it. The smaller
map is offset and rotated, but it still fits entirely on top of
the bigger map. Fred sticks a pin in the smaller map. The pin
goes all the way through to the bigger map. Sam is amazed! He
says “Wow! Do you realize that the position of that pin
represents the same place on BOTH maps?” Fred says “it’s really
not so amazing. There has to be one such point!”
Given the dimensions of a large map, and the offset, scale
and rotation of a smaller map that is entirely on top of the
larger map, find the single point that represents the same
place on both maps.
Input
There will be up to $500$ test cases in the input. Each
test case will consist of a single line with six integers:
w h x y
s r
The first two integers $w$ and $h$ ($0
< w, h \le 1\, 000$) are the width and height of the
larger map. The larger map will be on a plane, with the
southwest corner at the origin, the northwest corner at
$(0,h)$, the southeast
corner at $(w,0)$, and the
northeast corner at $(w,h)$.
The next two integers, $x$ and $y$ ($0
\le x \le w$, $0 \le y \le
h$), represent the $(x,y)$ coordinate on the plane of the
southwest corner of the smaller map.
The integer $s$
($0 < s < 100$)
represents the scale of smaller map as a percentage of the
larger map ($s=50$ means
that the smaller map has half the width and half the height of
the larger map).
The integer $r$
($0 \le r < 360$) is
the angle, in degrees, of counterclockwise rotation of the
smaller map around its southwest corner ($r=90$ means that the southeast corner
is rotated to be due north of the southwest corner).
The smaller map is guaranteed to lie completely within the
borders of the larger map. The input will end with a line with
six 0s.
Output
For each test case, output two real numbers, $x$ and $y$, representing the $(x,y)$ coordinate of the point where
both maps represent the same place. Output the numbers to two
decimal places of accuracy, with a single space between
them.
Sample Input 1 
Sample Output 1 
100 100 50 50 25 0
100 100 50 50 25 45
0 0 0 0 0 0

66.67 66.67
45.59 70.53
