Alice and Bob are playing the following game.

They choose two different positive integers K and L, and start the game with a tower of N coins. Alice always plays first, Bob – second, after that – Alice again, then Bob, and so on. They in turn can take 1, K or L coins from the tower.

The winner is who takes the last coin (or coins).

After a long, long playing, Alice realizes that there are cases in which she could win, no matter how Bob plays. And in all other cases Bob being careful can win, no matter how Alice plays.

Given N, K, L predict if Alice can win if both play optimally.

Constraints

1 <= K <= 20

1 <= L <= 20

1 <= N <= 1000000000

T <= 10^5

Input

First line contains T - number of cases,

Next T lines each contain 3 integer K, L, N.

Output

For each case print “Alice” (without quotes) if Alice can win, otherwise print “Bob” (without quotes).

Example

Input:
5
5 4 8
1 3 9
4 3 10
1 1 5
1 5 6
Output:
Bob
Alice
Alice
Alice
Bob