Alright, rephrasing it to "'null' or 'invalid' or 'not possible' in the context of the application of the problem"

The application of the problem (for solving a puzzle) did not require the k = 0 and n = 0 case because that case simply does not exist for the puzzle. I did not include k = 0 and n = 0 test case in the OJ on purpose, while setting the problem.

I agree with you on the fact the solution gets simple if you start looking at things from the base case.

PS: The puzzle is like Sudoku: 1 to 9 without 0's