Impressing Chefina

Chef has a matrix $A$ with $N$ rows (numbered $1$ through $N$) and $M$ columns (numbered $1$ through $M$); an element in row $i$ and column $j$ is denoted by $A_{i, j}$. He is going to play a game on this matrix with Chefina. In the game, Chef lists the elements of the matrix row by row in an alternating pattern, starting from the top left corner ― he writes down the first row from left to right,