A. Parkour Design
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.
Input

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

Output

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.

Example
Input
11
2 1
3 0
4 -1
4 1
14 1
1 -4
3 -1
2 10
24 -1
24 -3
8 4
Output
YES
YES
YES
NO
YES
NO
NO
NO
NO
YES
YES
Note

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.

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