MEX-ception

You are given two integers $N$ and $M$. You have to construct a matrix with $N$ rows and $M$ columns. Consider a multiset $S$ which contains $N + M$ integers: for each row and each column of this matrix, the MEX of the elements of this row/column belongs to $S$. Then, in the matrix you construct, the MEX of $S$ must be maximum possible. Note: The MEX of a multiset of integers is the smallest n