Simple

Because all the problems are so hard these days, this is a very simple problem.

Suppose you are given co-ordinates of two points $A$ and $B$ in 2D plane, an angle $M$ and a stick of length $L$. One end of the stick is in point $B$ and it creates $M$ degree angle with the line $AB$ in anti clockwise direction. It means that if one end of the stick is point $B$ and another end is point $C$ then angle $B$ is equal to $M$ and Length of $BC$ is equal to $L$. You have to tell the co-ordinates of the other end point of the stick, that is the co-ordinates of point $C$.

Input

First line will contains $T$ ($1 \le T \le 1000$), the number of test cases. Then for each of case, there will be a line containing 6 integers $Ax$, $Ay$, $Bx$, $By$ ($0 \le Ax,Ay,Bx,By \le 10000$, $Ax \le Bx$, $Ay \le By$), $M$ ($0 \le M \le 180$) and $L$ ($1 \le L \le 10000$).

Output

For each case, print two numbers $X$ and $Y$, the co-ordinates of the other end point of the stick rounded to the closest integer number in a line.

Sample

Input	Output
4 0 0 1 1 45 1 0 0 0 5 90 5 1 2 5 2 180 3 923 557 6907 5317 76 8111	1 0 5 5 8 2 10271 -2064
This diagram visualizes the first case in this test.