H. Warhead Games
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Alice and Bob are playing a game. They have a game board with $$$r$$$ rows and $$$c$$$ columns. The squares of the grid are either colored white or black. They start with a piece of sour candy placed in the first row and first column, corresponding to the top-left corner of the grid. They take turns, starting with Alice, and each player must either move the piece down (increasing the column number), to the right (increasing the row number), or diagonally down and right. However, they can't move the piece into a black square or off the grid. If a player cannot make a move, they lose. If both player play optimally, can you determine who wins?

Input

The first line contains two integer $$$r, c$$$ ($$$1 \leq r, c \leq 1000$$$) — the number of rows and number of columns in the grid, respectively.

The following $$$r$$$ lines contain a string $$$s_i$$$ of length $$$c$$$, where $$$s_{i, j}$$$ equals 'W' or 'B' — the color of the square in the $$$i$$$th row and $$$j$$$th column, where 'W' corresponds to white and 'B' corresponds to black.

It is guaranteed that the top-left corner of the grid is white.

Output

Print "Alice" (without the quotes) if Alice wins under optimal play, and print "Bob" otherwise.

Examples
Input
4 5
WBWBW
WWWWW
BWBWB
BWBWB
Output
Alice
Input
2 2
WB
BB
Output
Bob