AT_arc208_e [ARC208E] XY Game

You are given positive integers $ N $ , $ X $ , $ Y $ and a length- $ N $ integer sequence $ A=(A_1,A_2,\ldots,A_N) $ . There are $ N $ piles of stones, and the $ i $ -th pile $ (1\le i\le N) $ has $ A_i $ stones. Alice and Bob will play the following game using these piles: - Starting with Alice, the two players take turns alternately. - In each turn, the player chooses one non-empty pile and removes one or two stones from that pile. However, the player cannot make a move such that the number of stones in that pile becomes a multiple of $ X $ or a multiple of $ Y $ after removing stones. The player who cannot make a move first loses. Determine which player wins when both players play optimally. You are given $ T $ test cases, solve each of them.

The input is given from Standard Input in the following format: > $ T $ $ \text{case}_1 $ $ \text{case}_2 $ $ \vdots $ $ \text{case}_T $ Each test case is given in the following format: > $ N $ $ X $ $ Y $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $

Output the answers for each test case in order, separated by newlines. For each test case, print `Alice` if Alice wins when both players play optimally, and `Bob` if Bob wins.

### Sample Explanation 1 Consider the first test case. For example, the game proceeds as follows: - Alice removes two stones from the first pile. The first pile has two stones remaining. - Bob removes one stone from the second pile. The second pile has eleven stones remaining. - Alice removes one stone from the first pile. The first pile has one stone remaining. - Bob cannot make a move, so Bob loses and Alice wins. In this test case, Alice always wins no matter how both players make their moves. Therefore, print `Alice` on the first line. ### Constraints - $ 1\le T \le 2\times 10^5 $ - $ 1\le N \le 2\times 10^5 $ - The sum of $ N $ over all test cases is at most $ 2\times 10^5 $ . - $ 1\le X < Y\le 10^9 $ - $ 1\le A_i \le 10^{18} $ - All input values are integers.