Knight Game

시간 제한2초메모리 제한1024 MB

요약

H x W로 매우 큰 체스판의 (x,y)에서 나이트가 시작해, 갈 수 있는 방문하지 않은 칸으로 번갈아 이동하며 이동할 수 없는 쪽이 지는 게임의 승자를 판정한다.

문제

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.