Sum Game

Limits: 2 sec., 512 MiB

Ana and Bob play the following game.

First, Bob chooses a sequence of \(n\) positive integers \(a_1, a_2, \dots, a_n\). Then Ana is allowed to perform the following operations.

• She may erase any of the numbers from the sequence, but she is not allowed to erase all of them (at least one number must remain).

• For each remaining number, she may put either a + or a - sign in front of it.

After that, Ana computes the sum of the remaining numbers. She wins the game if she can obtain a sum that is divisible by \(m\). Otherwise, Bob wins.

Given \(n\) and \(m\), determine which player has a winning strategy.

Input

The first line contains a single integer \(t\) – the number of test cases.

Each of the next \(t\) lines contains two integers \(n\) and \(m\).

Output

For each test case, output a single line.

• Ana – if Ana has a winning strategy,

• Bob – if Bob has a winning strategy.

Constraints

\(1 \le t \le 10^5\),

\(1 \le n, m \le 10^{18}\).

Samples

Input (stdin) сopy	Output (stdout) сopy
3 1 2 2 3 3 8	Bob Ana Bob

Notes

In the first test case, Bob can choose \(a_1 = 3\).

In the second test case, no matter how Bob chooses \(a_1, a_2\), Ana has a winning strategy.