Catch Me If You Can

There is a grid of size $N \times M$. Let's denote the cell at the intersection of the $i$-th row and $j$-th column as $(i, j)$. Yahor and Alex are standing on this grid — Yahor in the cell $(1, 1)$, and Alex in the cell $(N, M)$. Yahor wants to catch Alex (to stay in the same cell with him), and Alex wants to avoid this. They are moving in turns, with the following rules: * Yahor moves first. *