Subtask 1

For this subtask, since $R=1$ and $C=1$, we can try and make only the first row and column a palindrome. One way to do this is to fill the first row and column with the letter a and fill the rest of the grid with the letter b.

Subtask 2

Because there are so few cases, it suffices to solve this subtask on paper and hardcode the answers. To reduce the amount of casework, notice that if we have a solution for $(R,C)$, we can get a solution for $(C,R)$ by flipping the grid.

Another possible approach is to write a brute force since there are only four important possibilities for each cell.

Subtask 3

This subtask is intended to aid students in thinking about the problem.

Subtask 4

The solutions to subtasks 1 and 2 should give some intuition here. From subtask 1, we propose the following general solution:

Fill the first $R$ rows and the first $C$ columns with the letter a and fill the rest of the grid with the letter b.

We notice that this fails when $R=0$, $C=0$, $R=N$ or $C=M$. We can handle these in pairs since we can flip the grid.

If $R=0$, we can fill the first $M-1$ columns with the letter a, and the last column with the letter b, and then increment the last $M-C$ characters of the last row. For instance, for the input 4 4 0 2 we can output:

aaab
aaab
aaab
aabc

If $R=N$, every row must be a palindrome. Because of this, starting from a full grid of a characters, we can easily reduce the number of palindromic columns by two at a time by making matching columns of the first row b characters. For instance, for the input 4 4 4 2, we can output:

baab
aaaa
aaaa
aaaa

However, this fails if $C$ is not the same parity as $M$, that is, if we cannot get $C$ by subtracting $2$ an integer number of times from $M$.

In this case, it depends: if $M$ is odd, we can use the middle column. For instance, for the input 5 5 5 2:

babab
aaaaa
aaaaa
aaaaa
aaaaa

However, the input 4 4 4 1 is impossible since there is no middle column.

We can handle $C=0$ and $C=M$ symmetrically by flipping the inputs, processing, and then flipping the output.