A14289 | Deleting Divisors
时间限制1s
内存限制256MB
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题目描述
Alice and Bob are playing a game.
They start with a positive integer $n$ and take alternating turns doing operations on it. Each turn a player can subtract from $n$ one of its divisors that isn't $1$ or $n$ . The player who cannot make a move on his/her turn loses. Alice always moves first.
Note that they subtract a divisor of the current number in each turn.
You are asked to find out who will win the game if both players play optimally.
They start with a positive integer $n$ and take alternating turns doing operations on it. Each turn a player can subtract from $n$ one of its divisors that isn't $1$ or $n$ . The player who cannot make a move on his/her turn loses. Alice always moves first.
Note that they subtract a divisor of the current number in each turn.
You are asked to find out who will win the game if both players play optimally.
输入格式
The first line contains a single integer $t$ ( $1 \leq t \leq 10^4$ ) — the number of test cases. Then $t$ test cases follow.
Each test case contains a single integer $n$ ( $1 \leq n \leq 10^9$ ) — the initial number.
Each test case contains a single integer $n$ ( $1 \leq n \leq 10^9$ ) — the initial number.
输出格式
For each test case output "Alice" if Alice will win the game or "Bob" if Bob will win, if both players play optimally.
输入输出样例
输入 #1
4 1 4 12 69
输出 #1
Bob Alice Alice Bob
In the first test case, the game ends immediately because Alice cannot make a move.
In the second test case, Alice can subtract $2$ making $n = 2$ , then Bob cannot make a move so Alice wins.
In the third test case, Alice can subtract $3$ so that $n = 9$ . Bob's only move is to subtract $3$ and make $n = 6$ . Now, Alice can subtract $3$ again and $n = 3$ . Then Bob cannot make a move, so Alice wins.
In the second test case, Alice can subtract $2$ making $n = 2$ , then Bob cannot make a move so Alice wins.
In the third test case, Alice can subtract $3$ so that $n = 9$ . Bob's only move is to subtract $3$ and make $n = 6$ . Now, Alice can subtract $3$ again and $n = 3$ . Then Bob cannot make a move, so Alice wins.
C++ 编辑器
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评测结果：Accepted