1-2-K Game

题意翻译

## 题目描述 现有n个东西，每次可以取1个，2个或k个 Alice和Bob轮流取，且Alice先取 问谁是最后一个取的 每组数据有t个询问 ## 输入输出格式 ### 输入格式： 第1行一个正整数t$(1<=t<=100)$ 第2到t+1行每行两个自然数n和k$(0<=n<=10^9,3<=k<=10^9)$ ### 输出格式： 共t行，每行输出`Alice`或`Bob`，表示赢家

题目描述

Alice and Bob play a game. There is a paper strip which is divided into $ n+1 $ cells numbered from left to right starting from $ 0 $ . There is a chip placed in the $ n $ -th cell (the last one). Players take turns, Alice is first. Each player during his or her turn has to move the chip $ 1 $ , $ 2 $ or $ k $ cells to the left (so, if the chip is currently in the cell $ i $ , the player can move it into cell $ i-1 $ , $ i-2 $ or $ i-k $ ). The chip should not leave the borders of the paper strip: it is impossible, for example, to move it $ k $ cells to the left if the current cell has number $ i<k $ . The player who can't make a move loses the game. Who wins if both participants play optimally? Alice and Bob would like to play several games, so you should determine the winner in each game.

输入输出格式

输入格式

The first line contains the single integer $ T $ ( $ 1<=T<=100 $ ) — the number of games. Next $ T $ lines contain one game per line. All games are independent. Each of the next $ T $ lines contains two integers $ n $ and $ k $ ( $ 0<=n<=10^{9} $ , $ 3<=k<=10^{9} $ ) — the length of the strip and the constant denoting the third move, respectively.

输出格式

For each game, print Alice if Alice wins this game and Bob otherwise.

输入输出样例

输入样例 #1

4
0 3
3 3
3 4
4 4

输出样例 #1

Bob
Alice
Bob
Alice