Alice and Bob

Alice and Bob are interested in playing games. One day, they invent a game which has rules below:
1. Firstly, Alice and Bob choose some random positive integers, and here we describe them as n, d₁, d₂,..., d_m.
2. Then they begin to write numbers alternately. At the first step, Alice has to write a “0”, here we let s₁ = 0 ; Then, at the second step, Bob has to write a number s₂ which satisfies the condition that s₂ = s₁ + d_k and s₂ <= n, 1<= k <= m ; From the third step, the person who has to write a number in this step must write a number s_i which satisfies the condition that s_i = s_i-1 + d_k or s_i = s_i-1 - d_k , and s_i-2 < s_i <= n, 1 <= k <= m, i >= 3 at the same time.
3. The person who can’t write a legal number at his own step firstly lose the game.
Here’s the question, please tell me who will win the game if both Alice and Bob play the game optimally.

At the beginning, an integer T indicating the total number of test cases.
Every test case begins with two integers n and m, which are described before. And on the next line are m positive integers d₁, d₂,..., d_m.
T <= 100;
1 <= n <= 10⁶;
1 <= m <= 100;
1 <= d_k <= 10⁶, 1 <= k <= m.

For every test case, print “Case #k: ” firstly, where k indicates the index of the test case and begins from 1. Then if Alice will win the game, print “Alice”, otherwise “Bob”.

2
7 1
3
7 2
2 6

Case #1: Alice
Case #2: Bob

standy from UESTC

2012 Multi-University Training Contest 8