#P1662H. Boundary
Boundary
Description
Bethany would like to tile her bathroom. The bathroom has width $w$ centimeters and length $l$ centimeters. If Bethany simply used the basic tiles of size $1 \times 1$ centimeters, she would use $w \cdot l$ of them.
However, she has something different in mind.
- On the interior of the floor she wants to use the $1 \times 1$ tiles. She needs exactly $(w-2) \cdot (l-2)$ of these.
- On the floor boundary she wants to use tiles of size $1 \times a$ for some positive integer $a$. The tiles can also be rotated by $90$ degrees.
For which values of $a$ can Bethany tile the bathroom floor as described? Note that $a$ can also be $1$.
Each test contains multiple test cases. The first line contains an integer $t$ ($1\le t\le 100$) — the number of test cases. The descriptions of the $t$ test cases follow.
Each test case consist of a single line, which contains two integers $w$, $l$ ($3 \leq w, l \leq 10^{9}$) — the dimensions of the bathroom.
For each test case, print an integer $k$ ($0\le k$) — the number of valid values of $a$ for the given test case — followed by $k$ integers $a_1, a_2,\dots, a_k$ ($1\le a_i$) — the valid values of $a$. The values $a_1, a_2, \dots, a_k$ have to be sorted from smallest to largest.
It is guaranteed that under the problem constraints, the output contains at most $200\,000$ integers.
Input
Each test contains multiple test cases. The first line contains an integer $t$ ($1\le t\le 100$) — the number of test cases. The descriptions of the $t$ test cases follow.
Each test case consist of a single line, which contains two integers $w$, $l$ ($3 \leq w, l \leq 10^{9}$) — the dimensions of the bathroom.
Output
For each test case, print an integer $k$ ($0\le k$) — the number of valid values of $a$ for the given test case — followed by $k$ integers $a_1, a_2,\dots, a_k$ ($1\le a_i$) — the valid values of $a$. The values $a_1, a_2, \dots, a_k$ have to be sorted from smallest to largest.
It is guaranteed that under the problem constraints, the output contains at most $200\,000$ integers.
Samples
3
3 5
12 12
314159265 358979323
3 1 2 3
3 1 2 11
2 1 2
Note
In the first test case, the bathroom is $3$ centimeters wide and $5$ centimeters long. There are three values of $a$ such that Bethany can tile the floor as described in the statement, namely $a=1$, $a=2$ and $a=3$. The three tilings are represented in the following pictures.
