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No.2059 Odd Move Nim

レベル : / AI推定難易度 : 1425 / 実行時間制限 : 1ケース 2.000秒 / メモリ制限 : 512 MB / 標準ジャッジ問題
タグ : （AC するまで非表示） / 解いたユーザー数 105
作問者 : nok0 / テスター : hir355 ぷら ygussany taiga0629kyopro
お気に入りにしたユーザー ProblemId : 7753 / 自分の提出
問題文最終更新日: 2022-08-21 19:11:03
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Problem Statement

There are piles of stones numbered from $1$ to $N$. Initially, pile $i$ contains $A_i$ stones.

Alice and Bob play a game using these piles. Starting with Alice, they alternately perform the following operation, and the player who cannot perform the operation loses.

  • Choose an integer $i$ between $2$ and $N$, inclusive, and an odd number $x$ that is at least $1$ and less than $i$. Choose $1$ or more stones from pile $i$ and move them to pile ${i-x}$.

Determine which player wins the game when both players act optimally.

Constraints

  • All input values are integers.
  • $2 \le N \le 200000$
  • $A_1 = 0$
  • $0 \le A_i< 2 ^ {30}\ (2\le i \le N)$

Input

$N$
$A_1$ $A_2$ $\ldots$ $A_N$

Output

Print Alice if Alice wins, and Bob if Bob wins.

Sample

Sample 1
Input
3
0 1 2
Output
Alice

By first moving $1$ stone from pile $2$ to pile $1$, Alice can always win.

Sample 2
Input
4
0 1 0 1
Output
Bob

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