Alice and Bob

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

Description

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,..., dm.
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 + dk 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 si which satisfies the condition that si = si-1 + dk or si = si-1 - dk , and si-2 < si <= 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.

Input

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,..., dm.
T <= 100;
1 <= n <= 106;
1 <= m <= 100;
1 <= dk <= 106, 1 <= k <= m.

Output

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”.

Sample Input

2
7 1
3
7 2
2 6

Sample Output

Case #1: Alice
Case #2: Bob

zhuyuanchen520

Source

2012 Multi-University Training Contest 8