GoG

Alice and Bob are playing GoG. GoG is a two-player board game. It consists of a grid with $n$ rows and $m$ columns. Players take alternate moves. In each move, a player can move in four directions (Up, Down, Left, and Right). If a player goes out of the grid or goes to a cell that has already been visited by any player (Alice or Bob), then the player dies. The last person alive wins.

Alice starts at the top-left cell and Bob starts at the bottom-right cell. Can you determine the winner, considering both players play optimally and Alice goes first?

Input

The first line of the input will contain a single integer $T$ ($1 \leq T \leq 100$), the number of test cases.

The next $T$ lines each will contain the two integers $n$ and $m$ ($1 \leq n, m \leq 10^5; 2 \leq n \times m \leq 10^5$), the dimensions of the grid for that testcase.

Output

For each testcase, print the name of the winner in a new line.

Sample

Input	Output
2 1 3 2 2	Alice Bob