Dear author, are you sure that answer ("NO") for the 1st example of input/output (
2 4
0 0 0
1 2 1
2 1 2
3 3 3
)
really correct?

Is it true that filling square as
0    1    3    2
2    3    1    0
3    2    0    1
1    0    2    3
is NOT correct magic square according to task rules?

You may swap top-left and top-right squares to get non-magic square
3 2 0 1
1 0 2 3
3 2 0 1
1 0 2 3

But if we fill square this way...
0 5 8 4
6 7 2 9
9 1 7 6
4 8 5 3

numbers are between 0 and n^2-1, so your example is incorrect!