Skinny Polygon

Two integers $x_{bb}$ and $y_{bb}$ are given. Call a polygon skinny when it satisfies all of the following conditions.

• It has 3 or 4 vertices.
• Two consecutive edges share only their common endpoint, and two edges that are not consecutive share no point at all.
• Both coordinates of every vertex are integers.
• Every vertex $(x, y)$ satisfies $0 \le x \le x_{bb}$ and $0 \le y \le y_{bb}$.
• At least one vertex has $x$-coordinate $0$, at least one has $x$-coordinate $x_{bb}$, at least one has $y$-coordinate $0$, and at least one has $y$-coordinate $y_{bb}$.
• Its area is at most $50000$.

A skinny polygon does not have to be convex. Several skinny polygons exist for one pair $(x_{bb}, y_{bb})$, so this problem asks for one of them, fixed as follows.

Let $g = \gcd(x_{bb}, y_{bb})$, $p = x_{bb}/g$ and $q = y_{bb}/g$. Define two quadrilaterals.

• $Q_1$: the integer $r$ with $1 \le r \le p$ and $rq \equiv 1 \pmod{p}$ is unique. Using that $r$ and $s = (rq-1)/p$, the vertices of $Q_1$ in order are $(0, 0)$, $(r, s)$, $(x_{bb}, y_{bb})$, $(p-r, q-s)$. The area of $Q_1$ is $g$.
• $Q_2$: the vertices of $Q_2$ in order are $(0, 0)$, $(x_{bb}, y_{bb}-1)$, $(p, q)$, $(x_{bb}-1, y_{bb})$. The area of $Q_2$ is $(p+q)/2$.

Both $Q_1$ and $Q_2$ are skinny. Print $Q_1$ when $2g \le p+q$, and $Q_2$ otherwise. The rule prints the one with the smaller area, and $Q_1$ when the two areas are equal.

The first line contains the number of test cases $n$ ($1 \le n \le 10^5$). Each of the next $n$ lines holds one test case. A line consists of two integers $x_{bb}$ and $y_{bb}$ ($2 \le x_{bb} \le 10^9$, $2 \le y_{bb} \le 10^9$).

For each test case print the answer in the following format.

4
x1 y1
x2 y2
x3 y3
x4 y4

The first line is the number of vertices, which is always $4$. The next four lines give the vertices in the order fixed in the statement, one vertex per line, with the two coordinates separated by a single space.