There is a chessboard with $n$ rows and $m$ columns. Some squares on the chessboard are broken. There are two knights on the chessboard, controlled by Alice and Bob. The movement of a knight is determined by two parameters $r$ and $c$. On each step, Alice or Bob can move their knight to a square which is $r$ squares away horizontally and $c$ squares vertically, or $r$ squares away vertically and $c$ squares horizontally.

Alice and Bob take turns playing, starting with Alice. On each turn, the player moves his or her knight. However, the player can not move the knight to a square which is broken or is occupied by the other knight.

There is an extra constraint. The configuration of the knights can be viewed as an ordered pair $(a,b)$ where $a$ is Alice’s square and $b$ is Bob’s square. It is forbidden to repeat a configuration which already occurred earlier.

A player loses if he or she can not make a move on his or her turn. Determine the winner if both players play optimally.

Input

The first line contains four integers $n$, $m$, $r$, and $c$ ($1 \le n,m \le 1000$, $0 \le r<n$, $0 \le c<m$).

Each of the following $n$ lines contains a string of length $m$. Together, these lines describe the chessboard. There are four types for each square:

• “@”: The square is broken.
• “.”: The square is not broken.
• “A”: The square is not broken. It is the start position of Alice’s knight.
• “B”: The square is not broken. It is the start position of Bob’s knight.

It is guaranteed that the squares “A” and “B” both occur exactly once on the chessboard.

Output

Output the name of the winner: “Alice” or “Bob”.

Examples

Input 1

2 3 1 2
A@.
B@.

Output 1

Alice

Note

On the first step, Alice moves the knight to the square $(2,3)$.

On the second step, Bob moves the knight to the square $(1,3)$.

On the third step, Alice moves the knight back to the square $(1,1)$.

On the fourth step, Bob can not move the knight back to the square $(2,1)$, because it will create the ordered pair of squares $(1,1),(2,1)$ which is the same as the position in the beginning. Alice wins.