KöMaL 2021 B5190

In a table of $n$ rows and $k$ columns, there is $-1$ written in each field. In each move, one row and one column is selected. Each number in the row is changed to the opposite, and then each number in the column is changed to the opposite. For what values of $n$ and $k$ is it possible to achieve a value of $+1$ in every field of the whole table?