Coloring the Grid

You are given a grid of size N x N, initially empty (represented by 0). Your task is to fill this grid with colors represented by integers from 1 to K. You can only color a cell if it is adjacent (horizontally or vertically) to the same color. Your goal is to count the number of valid ways to completely fill the grid. The input format is as follows: Input: N K Where N (1 <= N <= 10) is the size of the grid and K (1 <= K <= 5) is the number of colors. Output: An integer representing the number of valid ways to fill the grid. Example: Input: 2 2 Output: 8