Problem Description

Takahashi and Aoki decided to play a stone-taking game using a pile of $ N $ stones. The rules of the game are as follows:

• Players take turns removing one or more stones from the pile.
• The player who takes the last stone wins.

Takahashi, the first player, can remove up to $ A $ stones at a time, and Aoki, the second player, can remove up to $ B $ stones at a time.

Your task is to determine which player will win if both play optimally.

Input Format

The input is given from the standard input in the following format:

$ N $ $ A $ $ B $

• The first line contains an integer $N\ (1≦N≦10^{9})$ representing the number of stones.
• The second line contains two integers $A,B\ (1≦A,B≦10^{9})$ separated by a space, representing the maximum number of stones Takahashi and Aoki can remove at a time, respectively.

Output Format

Output Takahashi if the first player Takahashi wins, or Aoki if the second player Aoki wins. End the output with a newline.

Sample Input and Output

Sample Input #1

5
3 3

Sample Output #1

Takahashi

Sample Input #2

4
3 3

Sample Output #2

Aoki

Sample Input #3

5
3 2

Sample Output #3

Takahashi

Sample Input #4

1000000000
1000000000 1

Sample Output #4

Takahashi

Notes/Hints

Partial Points

This problem has partial points.

• If you correctly solve the dataset where $A\ =\ B$, you will be awarded $ 40 $ points.
• If you correctly solve the dataset where $A\ ≠\ B$, you will be awarded $ 60 $ points.
• By correctly solving both datasets, you will receive a total of $ 100 $ points.

Sample Explanation 1

• By taking $ 1 $ stone first, Takahashi can ensure victory regardless of how Aoki plays. - This case satisfies the constraint $A\ =\ B$.

Sample Explanation 2

• No matter how Takahashi plays, he cannot win. - This case satisfies the constraint $A\ =\ B$.

Sample Explanation 3

• By taking $ 2 $ stones first, Takahashi can ensure victory regardless of how Aoki plays. - This case satisfies the constraint $A\ ≠\ B$.

Sample Explanation 4

• By taking $ 1,000,000,000 $ stones first, Takahashi can ensure victory. - This case satisfies the constraint $A\ ≠\ B$.

见题面 Input 部分

见题面 Output 部分