Wallet Exchange (Codeforces 1919A)
Tags: Math, games

Alice and Bob are bored, so they decide to play a game with their wallets. Alice has $$$a$$$ coins in her wallet, while Bob has $$$b$$$ coins in his wallet.Both players take turns playing, with Alice making the first move. In each turn, the player will perform the following steps in order:  Choose to exchange wallets with their opponent, or to keep their current wallets.  Remove $$$1$$$ coin from the player's current wallet. The current wallet cannot have $$$0$$$ coins before performing this step. The player who cannot make a valid move on their turn loses. If both Alice and Bob play optimally, determine who will win the game.

Input: Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases. The description of the test cases follows.The first and only line of each test case contains two integers $$$a$$$ and $$$b$$$ ($$$1 \le a, b \le 10^9$$$) — the number of coins in Alice's and Bob's wallets, respectively.

Output: For each test case, output "Alice" if Alice will win the game, and "Bob" if Bob will win the game.

Note: In the first test case, an example of the game is shown below:  Alice chooses to not swap wallets with Bob in step 1 of her move. Now, $$$a=0$$$ and $$$b=1$$$.  Since Alice's wallet is empty, Bob must choose to not swap their wallets in step 1 of his move. Now, $$$a=0$$$ and $$$b=0$$$.  Since both Alice's and Bob's wallets are empty, Alice is unable to make a move. Hence, Bob wins. In the second test case, an example of the game is shown below:  Alice chooses to swap wallets with Bob in step 1 of her move. Now, $$$a=3$$$ and $$$b=1$$$.  Bob chooses to swap wallets with Alice in step 1 of his move. Now, $$$a=1$$$ and $$$b=2$$$.  Alice chooses to not swap wallets with Bob in step 1 of her move. Now, $$$a=0$$$ and $$$b=2$$$.  Since Alice's wallet is empty, Bob can only choose to not swap wallets with Alice in step 1 of his move. Now, $$$a=0$$$ and $$$b=1$$$.  Since Alice's wallet is empty, Alice can only choose to swap wallets with Bob in step 1 of her move. Now, $$$a=0$$$ and $$$b=0$$$.  Since both Alice's wallet and Bob's wallet are empty, Bob is unable to make a move. Hence, Alice wins. 

Sample Inputs:
10
1 1
1 4
5 3
4 5
11 9
83 91
1032 9307
839204 7281
1000000000 1000000000
53110 2024

Sample Outputs:
Bob
Alice
Bob
Alice
Bob
Bob
Alice
Alice
Bob
Bob

Solution (Python):
for i in range(int(input())):
    print(['Bob', 'Alice'][sum(list(map(int, input().split()))) % 2])

Solution (Python):
for s in [*open(0)][1:]:
    print(('Bob', 'Alice')[sum(map(int, s.split())) % 2])

Solution (Python):
for s in [*open(0)][1:]:
    print(('Bob', 'Alice')[sum(map(int, s.split())) % 2])