Problem G
Chocolate Division
Alf and Beata were two young adults living together a long, long time ago, before you could spend all your afternoons competing in programming. Their lives were thus much more boring than those of today’s young adults. How could you even survive back then, you might ask yourself. The answer is simple: you make your own chocolate bars! Our two cohabitants loved making chocolate bars, and often had huge piles of them each afternoon. To avoid filling their entire living room with chocolate bars, Beata challenged her friend to a game every evening to eat up all the chocolate – the Chocolate Division game.
The Chocolate Division game is played by two players (in our case, Alf and Beata) using a chocolate bar consisting of $R$ rows, each containing $C$ squares of chocolate. A move consists of splitting a rectangular piece of chocolate either horizontally or vertically into two pieces, such that the two new pieces again have integer height and width. The first move is performed on the original chocolate bar. Each subsequent move can performed on any piece of chocolate that has been split off so far, as long as it doesn’t have dimensions $1 \times 1$ (no split can be done on such a piece). Alf starts with the first move. If, at any point, a person can not perform their move because all remaining pieces have size $1 \times 1$ squares, that person loses.
Can you compute who wins the game, if both players play optimally?
Input
The first and only line contains the integers $R$ and $C$ ($1 \le R, C \le 500$), the height and width of the original chocolate bar.
Output
Output Alf if Alf wins the game, or Beata if Beata wins the game.
| Sample Input 1 | Sample Output 1 |
|---|---|
1 1 |
Beata |
| Sample Input 2 | Sample Output 2 |
|---|---|
1 2 |
Alf |
| Sample Input 3 | Sample Output 3 |
|---|---|
2 2 |
Alf |
