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B - Counterclockwise Rotation

Score : $200$ points

Problem Statement

In an $xy$-coordinate plane whose $x$-axis is oriented to the right and whose $y$-axis is oriented upwards, rotate a point $(a, b)$ around the origin $d$ degrees counterclockwise and find the new coordinates of the point.

Constraints

• $-1000 \leq a,b \leq 1000$
• $1 \leq d \leq 360$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$a$ $b$ $d$

Output

Let the new coordinates of the point be $(a', b')$. Print $a'$ and $b'$ in this order, with a space in between.
Your output will be considered correct when, for each value printed, the absolute or relative error from the answer is at most $10^{-6}$.

2 2 180

-2 -2

When $(2, 2)$ is rotated around the origin $180$ degrees counterclockwise, it becomes the symmetric point of $(2, 2)$ with respect to the origin, which is $(-2, -2)$.

5 0 120

-2.49999999999999911182 4.33012701892219364908

When $(5, 0)$ is rotated around the origin $120$ degrees counterclockwise, it becomes $(-\frac {5}{2} , \frac {5\sqrt{3}}{2})$.
This sample output does not precisely match these values, but the errors are small enough to be considered correct.

0 0 11

0.00000000000000000000 0.00000000000000000000

Since $(a, b)$ is the origin (the center of rotation), a rotation does not change its coordinates.

15 5 360

15.00000000000000177636 4.99999999999999555911

A $360$-degree rotation does not change the coordinates of a point.

-505 191 278

118.85878514480690171240 526.66743699786547949770