Score : $400$ points

问题描述

Takahashi 和 Aoki 正在玩一个游戏。

• 首先，Takahashi 在 $A$ 和 $B$（包含端点）之间选择一个整数并告诉 Aoki。
• 接着，Aoki 在 $C$ 和 $D$（包含端点）之间选择一个整数。
• 如果这两个整数之和是质数，则 Aoki 获胜；否则，Takahashi 获胜。

当两位玩家都采取最优策略时，哪位玩家会获胜？

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Takahashi and Aoki are playing a game.

• First, Takahashi chooses an integer between $A$ and $B$ (inclusive) and tells it to Aoki.
• Next, Aoki chooses an integer between $C$ and $D$ (inclusive).
• If the sum of these two integers is a prime, then Aoki wins; otherwise, Takahashi wins.

When the two players play optimally, which player will win?

Constraints

• $1 \leq A \leq B \leq 100$
• $1 \leq C \leq D \leq 100$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$A$ $B$ $C$ $D$

Output

If Takahashi wins when the two players play optimally, print Takahashi; if Aoki wins, print Aoki.

Sample Input 1

2 3 3 4

Sample Output 1

Aoki

For example, if Takahashi chooses $2$, Aoki can choose $3$ to make the sum $5$, which is a prime.

Sample Input 2

1 100 50 60

Sample Output 2

Takahashi

If they play optimally, Takahashi always wins.

Sample Input 3

3 14 1 5

Sample Output 3

Aoki

update @ 2024/3/10 10:19:02