Where am I
I am a ball on a circle table. The table's surface is so smooth that I can move without energy lost.
Now you are to give me a hit vector, I want to know where I will be after T seconds. Collisions between me and the edge of the table satisfy Conservation of Momentum Theorem , also my speed after collision is as fast as before. Look for the figure below to know it more clearly:
The first line contains a number N, the number of test cases you have to proceed.
Each test case has three lines.First line has three numbers, x1,y1,r1, the center and radius of the table. Second line has x2,y2,r2, the parameters of me (the ball). The third line consists of dx, dy, T: (dx,dy) is the hit vector, T is the time I have moved since you hit me. To explain hit vector: if I am at position (x0,y0) now ,next second I will be at position (x0+dx,y0+dy) without conllision. All input numbers are non-negative integer and less than 10^6.Also you can assume the ball must be in the table.
Please output two float number x , y,which mean the center position of the ball after T seconds and round to just one decimal places.
5 5 10
5 5 1
1 0 30
1 1 10
1 0 2
1 1 100