1914 - Cyclically Rotating a Grid.

Medium

You are given an m x n integer matrix grid, where m and n are both even integers, and an integer k.

The matrix is composed of several layers, which is shown in the below image, where each color is its own layer:

A cyclic rotation of the matrix is done by cyclically rotating each layer in the matrix. To cyclically rotate a layer once, each element in the layer will take the place of the adjacent element in the counter-clockwise direction. An example rotation is shown below:

Return the matrix after applying k cyclic rotations to it.

Example 1:

Input: grid = [40,10,30,20], k = 1

Output: [10,20,40,30]

Explanation: The figures above represent the grid at every state.

Example 2:

Input: grid = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16], k = 2

Output: [3,4,8,12,2,11,10,16,1,7,6,15,5,9,13,14]

Explanation: The figures above represent the grid at every state.

Constraints:

• m == grid.length

• n == grid[i].length

• 2 <= m, n <= 50

• Both m and n are even integers.

• 1 <= grid[i][j] <= 5000

• <code>1 <= k <= 10⁹</code>