4497: H. GameX

Once upon a time, there were two saints named St. Alice and St. Bob.
Being saints were quite boring, so they decided to play a game. The game was about the MEX operation, and was therefore named GameX.
To help you, a mere mortal, to understand the game, we first present the definition of MEX. Given a set S of integers, define  MEX(S) as the smallest natural number which is not in S. In other words,  MEX(S)=min{x∈N∣x∉S}.
The game went as follows.
Before the game started, S={a₁,a₂,⋯,a_n}, which contained the Secret of Life, the Universe and Everything.
The two saints moved alternately, with St. Alice being the first. During one's move, he/she could choose an arbitrary integer x, and insert x into S. So S is updated to S∪ {x}.
After k rounds, each player made k updates, and now it's time to decide the winner. St. Alice wins iff MEX(S) is even, and Bob wins otherwise.
Saints are very smart, so both of them made optimal moves. Can a mortal like you decide the winner?

The first line contains a positive integer T (1 ≤ T ≤ 10⁴), denoting the number of testcases.
For each testcase:

• The first line contains two integers n,kn,k (1≤n,k≤2×10⁵), denoting the size of S before the game started and the number of rounds.
• The next line contains n distinct natural numbers a₁,a₂,⋯,a_n (0≤a_i≤10⁶), denoting S.

It is guaranteed that ∑ n, ∑ k ≤ 2× 10⁵.

For each testcase, output one line consisting of the name of the winner. If St. Alice won output Alice, otherwise output Bob.

5
14 5
7 13 1 6 14 2 16 17 18 19 34 36 20 23
13 5
8 10 3 13 14 15 16 17 18 19 20 36 38
14 5
14 20 12 6 0 16 8 11 9 17 13 3 5 19
14 5
15 7 13 3 1 17 16 14 0 12 4 10 22 53
14 5
7 3 4 0 14 15 16 17 18 19 20 21 22 23

Bob
Bob
Alice
Bob
Alice