Educational Codeforces Round 68 D 1-2-K Game

Problem

time limit per test : 2 seconds
memory limit per test : 256 megabytes
input : standard input
output : standard output

Description

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.

Input

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 ≤ 109, 3 ≤ k ≤ 109) — the length of the strip and the constant denoting the third move, respectively.

Output

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

Example

input

1
2
3
4
5
4
0 3
3 3
3 4
4 4

output

1
2
3
4
Bob
Alice
Bob
Alice

Solution

Idea

打表找规律,存在循环。

发现若 k 不为 3 的倍数,则循环节长度为3 。若 k 为 3 的倍数, 循环节长度为 k+1, 循环节内也有一定的规律。

❤采之欲遗谁,所思在远道。❤
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