CF2202A Parkour Design

Today, Alex wants to build a parkour course for Steve to train his parkour skills on. A parkour course is a sequence $ p_0 \to p_1 \to \ldots \to p_k $ of integer coordinates on the plane. Here, a contiguous pair of coordinates is called a move, denoted as $ p_{i-1} \to p_i $ . Alex knows that Steve can only perform the following types of moves: - $ (x_i,y_i) \to (x_i+2,y_i+1) $ ; - $ (x_i,y_i) \to (x_i+3,y_i) $ ; - $ (x_i,y_i) \to (x_i+4,y_i-1) $ . Note that Steve will not perform any other type of moves. For example, Steve can perform $ (0,0) \to (2,1) $ and $ (2,1) \to (5,1) $ , but will never perform moves such as $ (2,1) \to (3,2) $ , $ (3,0) \to (5,-1) $ , or $ (4,-1) \to (6,-1) $ (even though they may look very easy). You are given an integer coordinate $ (x,y) $ on the plane. Please determine if it is possible to make a parkour course $ q_0,q_1,\ldots,q_k $ that satisfies the following conditions: - $ q_0=(0,0) $ ; - $ q_k=(x,y) $ ; - The parkour course only consists of moves that Steve can perform.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^3 $ ). The description of the test cases follows. The only line of each test case contains two integers $ x $ and $ y $ ( $ 1 \le x \le 10^9 $ , $ -10^8 \le y \le 10^8 $ ).

If it is possible to make a parkour course that satisfies the conditions, output "YES" on a separate line. If it is impossible to make a parkour course that satisfies the conditions, output "NO" on a separate line. You can output the answer in any case. For example, the strings "yEs", "yes", and "Yes" will also be recognized as positive responses.

For the fifth test case, the parkour course must start from $ (0,0) $ and end on $ (14,1) $ . This can be achieved by the following parkour course. $$$ (0,0) \to (4,-1) \to (7,-1) \to (9,0) \to (12,0) \to (14,1) $$$ Note that the following parkour course does not satisfy the third condition stated above due to the moves highlighted in red. $$$ (0,0) \to \color{red}{(4,-1) \to (6,-1)} \to (8,0) \to \color{red}{(11,0) \to (14,1)} $$$