AT_arc229_d [ARC229D] Nim_k ?

There are $ K+1 $ piles of stones. The $ i $ -th pile has $ A_i $ stones. Alice and Bob play a game. In this game, they alternately take turns with Alice moving first. On each turn, the following operation is performed exactly $ K $ times. - Choose a pile with one or more stones, and remove one or more stones from it. Here, the same pile may be chosen multiple times within the same turn. The player who is unable to perform the operation $ K $ times on their own turn loses the game. 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 $ $ \mathrm{case}_1 $ $ \mathrm{case}_2 $ $ \vdots $ $ \mathrm{case}_T $ Each test case $ \mathrm{case}_t $ is given in the following format: > $ K $ $ A_1 $ $ A_2 $ $ \dots $ $ A_{K+1} $

Output $ T $ lines. The $ i $ -th line should contain `Alice` if Alice wins when both players play optimally for the $ i $ -th test case, and `Bob` if Bob wins.

### Sample Explanation 1 Consider the first test case. For example, suppose Alice performs the following operations on her first turn. - Choose the second pile, and remove two stones from it. The number of stones in the second pile becomes $ 0 $ . - Choose the third pile, and remove three stones from it. The number of stones in the third pile becomes $ 0 $ . After her turn ends, only one stone remains. Therefore, Bob cannot perform the operation twice, so Alice wins. In the second test case, every time Alice removes stones from one pile, Bob can remove the same number of stones from the other pile. By acting in this way, Bob can win. ### Constraints - $ 1 \leq T \leq 2 \times 10^5 $ - $ 1 \leq K \leq 2 \times 10^5 $ - $ 1 \leq A_i \leq 10^9 $ - The sum of $ K $ over all test cases is at most $ 2 \times 10^5 $ . - All input values are integers.