Boundary

Bethany would like to tile her bathroom. The bathroom has width $w$ centimeters and length $l$ centimeters. If Bethany uses only basic $1 \times 1$ centimeter tiles, she needs $w \cdot l$ of them.

She has something else in mind.

• On the interior of the floor, she uses $1 \times 1$ tiles. She needs exactly $(w - 2) \cdot (l - 2)$ of these.
• On the floor boundary, she uses 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. Each of the following $t$ lines contains two integers $w$ and $l$ ($3 \le w, l \le 10^9$), the dimensions of the bathroom.

For each test case, print an integer $k$ ($0 \le k$), the number of valid values of $a$, followed by the $k$ valid values $a_1, a_2, \dots, a_k$ in increasing order. It is guaranteed that under the problem constraints, the output contains at most $200\,000$ integers.