Dr. Xenovian's specialized computer architecture

Description
Dr. Xenovian's specialized computer architecture has taken off (it turns out that is really well-suited for mining gigabyte coins), and her technical prowess has caught the attention of RUST Corp., an interplanetary mining company. RUST Corp. has hired Dr. Xenovian to "consult on a TOP SECRET hardware problem". After signing a non-disclosure agreement, Dr. Xenovian is flown to a high-security warehouse in Olympus City that is filled with alledgely-alien monoliths of all different shapes and sizes that RUST Corp. has collected during their mining expeditions.

Each monolith has matrix of integer values, and every 36 seconds, the values rotate in an anti-clockwise direction on the monolith's surface as shown in the example below.



Note that in one rotation, elements shift by one step only. The first step to decoding these mysterious monoliths is to write a program capable of predicting the state of a matrix after an arbitrary number of rotations ( r ). Your task is to write this program.

All monolith-matrices are such that the minimum of m and n will be even.

As an example, rotate the Start matrix by 2:

Start         First           Second
 1 2 3 4       2  3  4  5      3  4  5  6
12 1 2 5  =>   1  2  3  6 =>   2  3  4  7
11 4 3 6      12  1  4  7      1  2  1  8
10 9 8 7      11 10  9  8     12 11 10  9
Function Description

Complete the monolithRotation function. It should print the resultant 2D integer array and return nothing.

monolithRotation has the following parameters:

matrix: a 2D array of integers
r : an integer that represents the rotation factor
Input Format

The first line contains three space-separated integers, m, n, and r (rows, columns, and rotations respectively).

The next m lines contain n space-separated integers, representing the elements of a row of matrix.

Constraints

2 ≤ m, n ≤ 300
1 ≤ r ≤ 109
min(m,n) % 2 = 0
1 ≤ aij ≤ 109 where i ∈ [1...m] and j ∈ [1...n]
Output Format

Print each row of the rotated matrix as space-separated integers on separate lines.

Example 0
Sample Input

4 4 2
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
Sample Output

3 4 8 12
2 11 10 16
1 7 6 15
5 9 13 14
Explanation

The matrix is rotated through two rotations.

 1  2  3  4      2  3  4  8      3  4  8 12
 5  6  7  8      1  7 11 12      2 11 10 16
 9 10 11 12  ->  5  6 10 16  ->  1  7  6 15
13 14 15 16      9 13 14 15      5  9 13 14
Example 1
Sample Input

5 4 7
1 2 3 4
7 8 9 10
13 14 15 16
19 20 21 22
25 26 27 28
Sample Output

28 27 26 25
22 9 15 19
16 8 21 13
10 14 20 7
4 3 2 1
Explanation

The various states through 7 rotations:

1  2  3  4      2  3  4 10    3  4 10 16    4 10 16 22
7  8  9 10      1  9 15 16    2 15 21 22    3 21 20 28
13 14 15 16 =>  7  8 21 22 => 1  9 20 28 => 2 15 14 27 =>
19 20 21 22    13 14 20 28    7  8 14 27    1  9  8 26
25 26 27 28    19 25 26 27    13 19 25 26   7 13 19 25

10 16 22 28    16 22 28 27    22 28 27 26    28 27 26 25
 4 20 14 27    10 14  8 26    16  8  9 25    22  9 15 19
 3 21  8 26 =>  4 20  9 25 => 10 14 15 19 => 16  8 21 13
 2 15  9 25     3 21 15 19     4 20 21 13    10 14 20  7
 1  7 13 19     2  1  7 13     3  2  1  7     4  3  2  1
Example 2
Sample Input

2 2 3
1 1
1 1
Sample Output

1 1
1 1
Explanation

All of the elements are the same, so any rotation will repeat the same matrix.