E. Min Nim
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

Alice and Bob are playing a game with a pile of $$$n$$$ stones.

They alternate turns removing stones from the pile, with Alice moving first. On her first turn, Alice must remove between $$$1$$$ and $$$k$$$ stones (inclusive).

On subsequent turns, if the previous player removed exactly $$$x$$$ stones, the next player must remove between $$$1$$$ and $$$x$$$ stones (inclusive).

The player who removes the last stone wins. Determine who wins if both players play optimally.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^5$$$). The description of the test cases follows.

The only line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1\le k\le n\le 10^{18}$$$) — the initial number of stones and the maximum number of stones Alice may remove on her first turn.

Output

For each test case, output the winner if both players play optimally.

Example
Input
6
6 1
6 2
12 3
12 4
67676767676768 1
67676767676769 67676767676768
Output
Bob
Alice
Bob
Alice
Bob
Alice