P15715 [JAG 2023 Summer Camp #2] Knight Game

The rule of this game is given as follows. - There is a knight and a chessboard with $H$ rows and $W$ columns. The square at the $i$-th row from the top and the $j$-th column from the left is called square $(i, j)$. Initially, the knight is placed on square $(x, y)$. - Alice and Bob alternately take the following action, starting with Alice. - Move the knight onto one of the unvisited squares according to the knight's movement. - Knights can move from $(x_1, y_1)$ to $(x_2, y_2)$ if and only if $(x_1 - x_2)^2 + (y_1 - y_2)^2$ is $5$. - The player who cannot move the knight is the loser. When both players have done their best, determine whether Alice or Bob will win. Answer for $T$ test cases. The unvisited square is defined as follows. - A square on the board that the knight has never visited since the beginning of the game.

$$ \begin{aligned} &T \\ &case_1 \\ &\vdots \\ &case_T \end{aligned} $$ $case_i$ represents the $i$-th test case. Each test case is given in the following format. $$H \ W \ x \ y$$ The input satisfies the following constraints. - All inputs consist of integers. - $1 \leq T \leq 2 \times 10^5$ - $1 \leq H, W \leq 10^9$ - $1 \leq x \leq H$ - $1 \leq y \leq W$

Output $T$ lines. On the line $i$, answer the winner of the $i$-th test case, Alice or Bob.