Problem Statement

You are given positive integers $N$, $X$, $Y$ and a length-$N$ integer sequence $A=(A_1,A_2,\ldots,A_N)$.

There are $N$ piles of stones, and the $i$-th pile $(1\le i\le N)$ has $A_i$ stones.

Alice and Bob will play the following game using these piles:

• Starting with Alice, the two players take turns alternately.
• In each turn, the player chooses one non-empty pile and removes one or two stones from that pile. However, the player cannot make a move such that the number of stones in that pile becomes a multiple of $X$ or a multiple of $Y$ after removing stones.

The player who cannot make a move first loses.

Determine which player wins when both players play optimally.

You are given $T$ test cases, solve each of them.

Constraints

• $1\le T \le 2\times 10^5$
• $1\le N \le 2\times 10^5$
• The sum of $N$ over all test cases is at most $2\times 10^5$.
• $1\le X < Y\le 10^9$
• $1\le A_i \le 10^{18}$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
\text{case}_1
\text{case}_2
\vdots
\text{case}_T

Each test case is given in the following format:

N X Y
A_1 A_2 \ldots A_N

Output

Output the answers for each test case in order, separated by newlines.

For each test case, print Alice if Alice wins when both players play optimally, and Bob if Bob wins.