9119: Puzzle: Square Jam

Grammy is a puzzle master. Today, she is playing a variant of "Square Jam" puzzle. Given an $n\times m$ rectangle. The goal is to divide the rectangle into several squares (with integral lengths) such that no point is touched by 4 squares.



The left picture illustrates a solution to a $4\times 6$ puzzle, and the right picture shows an example of what is not allowed in the solution.

Grammy surely knows how to solve the puzzle, but she decided to give you a quiz. Please solve the puzzle.

There are multiple test cases.
The first line contains the number of test cases $T$ (1≤T≤2×1051 \leq T \leq 2\times 10^51≤T≤2×105).
Each of the following $T$ lines contains two positive integers $n,m$ (1≤n,m≤1051 \leq n,m \leq 10^51≤n,m≤105), denoting the side lengths of the rectangle.
It is guaranteed that the sum of $nm$ is less than or equal to 2×1052\times 10^52×105.

For each test case:
If the solution does not exist, output "$\text{NO}$" on a single line.
Otherwise, output "$\text{YES}$" on the first line, then output an integer $k$ on the second line, denoting the number of squares divided. Finally, output $k$ lines, each of which contains $3$ integers x,y,lx,y,lx,y,l, denoting a square of size $l$ having (x,y)(x,y)(x,y) as its upper-left corner.
For the details of the coordinates, please refer to the following picture. 

2
4 6
1 1

YES
10
0 0 2
0 2 1
1 2 1
0 3 3
2 0 1
3 0 1
2 1 2
3 3 1
3 4 1
3 5 1
YES
1
0 0 1