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 1\,000)~.
The next ~T~ lines will each contain 7 real numbers to 6 decimal places, ~x\ y\ z\ rx\ ry\ rz\ \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 ~1\,000~ 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', y', z')~, 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