Problem A
Alex and Barbossa
Alex and Barbossa, owners of the largest collection of unlabelled cards in the seven seas, are planning a fun game to pass the time during a lull of the ocean. Their first idea was no good, once they eventually realized that the winning strategy was so simple that a 51-character Ruby script could find the winning player. They’ve come up with a new version which is sure to make the game more interesting.
The new game is as follows: there is a stack of $k$ cards on the table. Alex and Barbossa take turns taking either $m$ or $n$ cards, beginning with Alex. The first player with no valid moves left loses.
Given $k$, $m$, and $n$, determine which player will win the game provided that both play with an optimal strategy.
Inputs
The input consists of a single line containing three space-separated integers $1 \leq k \leq 2 \cdot 10^9$ and $1 \leq m \leq n \leq 2 \cdot 10^9$.
Outputs
On a single line output the name of the winning player.
| Sample Input 1 | Sample Output 1 |
|---|---|
5 2 2 |
Barbossa |
| Sample Input 2 | Sample Output 2 |
|---|---|
25 3 10 |
Alex |
| Sample Input 3 | Sample Output 3 |
|---|---|
2 1 3 |
Barbossa |
