Apples and Bananas

Time limit1sMemory limit128 MB

Summary

Decide the winner of an alternating game where each move removes one apple, one banana, three apples and one banana, or one apple and three bananas from piles of a apples and b bananas.

Level: Medium7 of 10
Topics: Game theory, Dynamic programming, Math
Solved: No attempts yet

Problem

Alice and Bob play a game with a pile of $a$ apples and $b$ bananas. Alice moves first, and the two alternate turns. On a turn a player removes exactly one of the following combinations: $1$ apple, $1$ banana, $3$ apples and $1$ banana, or $1$ apple and $3$ bananas. A move is legal only when the pile holds at least that many of each fruit. The player who removes the last fruit wins. When the pile starts empty, Bob wins at once. Given the numbers of apples and bananas and optimal play from both sides, decide whether Alice or Bob wins.

Input

The input holds the apple count $a$ and the banana count $b$ , separated by a space. Both satisfy $0 \le a, b \le 1000$ .

Output

Print the name of the winner under optimal play, either Alice or Bob.

Examples3

Example 1
Input
```
1 0
```
Expected output
```
Alice
```
Example 2
Input
```
2 2
```
Expected output
```
Bob
```
Example 3
Input
```
3 4
```
Expected output
```
Bob
```