30363번 - Knight Game 다국어

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.

$T$

$\text{case}_1$

$\vdots$

$\text{case}_T$

$\text{case}_i$ represents the $i$-th test case.

Each test case is given in the following format.

$H$ $W$ $x$ $y$

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

• All inputs consist of integers.
• $1 \le T \le 2 \times 10^5$
• $1 \le H, W \le 10^9$
• $1 \le x \le H$
• $1 \le y \le W$