CF1662H.Boundary

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 $1$.

贝丝妮想用瓷砖铺满她的浴室。浴室的宽度为 $w$ 厘米，长度为 $l$ 厘米。如果贝丝妮仅使用基本的 $1 \times 1$ 厘米瓷砖，则总共需要 $w \cdot l$ 块。

然而，她另有打算：

• 在地板内部区域，她打算使用 $1 \times 1$ 的瓷砖，恰好需要 $(w-2) \cdot (l-2)$ 块；
• 在地板边界区域，她打算使用尺寸为 $1 \times a$ 的瓷砖（其中 $a$ 为某个正整数），且这些瓷砖可沿 $90^\circ$ 方向旋转。

对于哪些 $a$ 的取值，贝丝妮能按上述方式铺满整个浴室地板？注意：$a$ 也可以等于 $1$。

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.

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1\le t\le 100$），表示测试用例的数量。接下来是 $t$ 个测试用例的描述。

每个测试用例由一行组成，包含两个整数 $w$、$l$（$3 \leq w, l \leq 10^{9}$），表示浴室的尺寸。

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.

对于每个测试用例，输出一个整数 $k$（$0\le k$）—— 表示该测试用例下合法的 $a$ 值的个数 —— 然后输出 $k$ 个整数 $a_1, a_2,\dots, a_k$（$1\le a_i$）—— 即所有合法的 $a$ 值。这些值 $a_1, a_2, \dots, a_k$ 必须按从小到大的顺序排列。

在本题约束条件下，保证输出中整数的总数不超过 $200\,000$ 个。

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.

在第一个测试用例中，浴室宽 $3$ 厘米、长 $5$ 厘米。存在三个满足题干所述条件的 $a$ 值，使得贝丝妮能够按要求铺满地面，即 $a=1$、$a=2$ 和 $a=3$。这三种铺法如以下图片所示。