Your task is simple: given some points in 3D, rotate them around an axis of rotation.

Input Specification

The first line of input will contain $T$, the number of test cases $(1\le T\le 1000)$.
The next $T$ lines will each contain 7 real numbers to 6 decimal places, $xyzrxryrz\theta$. You are to rotate the point $(x,y,z)$ around the axis of rotation $(rx,ry,rz)$ such that if you look at the origin from the axis of rotation, it will be rotated $\theta$ radians counterclockwise. All coordinates will have absolute value of at most $1000$ and $\theta$ will be such that $0\le \theta <2\pi$. It is guaranteed at least one of $rx,ry,rz$ is nonzero.

Output Specification

Output $T$ lines, each line should have the $(x^{\prime },y^{\prime },z^{\prime })$, the result of rotation as three space-separated real numbers. Your answer will be judged as correct if it is within an absolute or relative error of ${10}^{-6}$.

Sample Input

2
0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 3.141593
1.000000 0.000000 0.000000 1.000000 1.000000 1.000000 1.570796

Sample Output

0.000000 0.000000 0.000000
0.333334 0.910683 -0.244017