题目描述

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 $1$ .

输入格式

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.

输出格式

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.

3
3 5
12 12
314159265 358979323

3 1 2 3
3 1 2 11
2 1 2

提示

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.