9548: ABC239 —— D - Prime Sum Game
[Creator : ]
Description
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?
- 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?
Input
Input is given from Standard Input in the following format:
```
$A$ $B$ $C$ $D$
```
```
$A$ $B$ $C$ $D$
```
Output
If Takahashi wins when the two players play optimally, print `Takahashi`; if Aoki wins, print `Aoki`.
Constraints
- $1 \leq A \leq B \leq 100$
- $1 \leq C \leq D \leq 100$
- All values in input are integers.
- $1 \leq C \leq D \leq 100$
- All values in input are integers.
Sample 1 Input
2 3 3 4
Sample 1 Output
Aoki
For example, if Takahashi chooses 2, Aoki can choose 3 to make the sum 5, which is a prime.
Sample 2 Input
1 100 50 60
Sample 2 Output
Takahashi
If they play optimally, Takahashi always wins.
Sample 3 Input
3 14 1 5
Sample 3 Output
Aoki