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.

今天，Alex 想为 Steve 设计一个跑酷训练课程。一个跑酷课程是一组平面上的整数坐标序列 $p_0 \to p_1 \to \ldots \to p_k$。其中，相邻两个坐标构成一次“移动”，记作 $p_{i-1} \to p_i$。

Alex 知道 Steve 只能执行以下三种类型的移动：

• $(x_i,y_i) \to (x_i+2,y_i+1)$；
• $(x_i,y_i) \to (x_i+3,y_i)$；
• $(x_i,y_i) \to (x_i+4,y_i-1)$。

注意：Steve 不会执行任何其他类型的移动。例如，Steve 可以执行 $(0,0) \to (2,1)$ 和 $(2,1) \to (5,1)$，但绝不会执行如 $(2,1) \to (3,2)$、$(3,0) \to (5,-1)$ 或 $(4,-1) \to (6,-1)$ 这样的移动（即使它们看起来非常简单）。

你将获得平面上的一个整数坐标 $(x,y)$。

请判断是否存在一个跑酷课程 $q_0,q_1,\ldots,q_k$，满足以下条件：

• $q_0=(0,0)$；
• $q_k=(x,y)$；
• 该跑酷课程仅由 Steve 能够执行的移动组成。

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 $y$ ($1 \le x \le 10^9$, $-10^8 \le y \le 10^8$).

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 10^3$）。随后是测试用例的描述。

每个测试用例仅有一行，包含两个整数 $x$ 和 $y$（$1 \le x \le 10^9$，$-10^8 \le y \le 10^8$）。

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.

如果可以构造出满足条件的跑酷课程，则在单独一行输出“YES”。

如果无法构造出满足条件的跑酷课程，则在单独一行输出“NO”。

你可以以任意大小写形式输出答案。例如，字符串 “yEs”、“yes” 和 “Yes” 也会被识别为肯定回答。

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.

$$(0,0) \\to \\color{red}{(4,-1) \\to (6,-1)} \\to (8,0) \\to \\color{red}{(11,0) \\to (14,1)}$$

对于第五个测试用例，跑酷路线必须从 $(0,0)$ 开始，并在 $(14,1)$ 结束。

以下跑酷路线可满足该要求：

$$(0,0) \\to (4,-1) \\to (7,-1) \\to (9,0) \\to (12,0) \\to (14,1)$$

注意：以下跑酷路线因红色高亮标出的移动步骤，不满足上述第三条条件：

$$(0,0) \\to \\color{red}{(4,-1) \\to (6,-1)} \\to (8,0) \\to \\color{red}{(11,0) \\to (14,1)}$$