Table Game

Alice and Bob are playing a game with a $(N+1)\times (M+1)$ table. Let's denote the cell in the $i$-th row and $j$-th column ($0 \le i \le N$, $0 \le j \le M$) by $(i, j)$. The rules of the game are: - At the beginning, a stone is placed in some cell of the table. - The players alternate turns, Alice goes first. - In each turn, the current player must move the stone from its current cell (let'