Boundary

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 $ .

输入输出格式

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.

输入输出样例

输入样例 #1

3
3 5
12 12
314159265 358979323

输出样例 #1

3 1 2 3
3 1 2 11
2 1 2

说明

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.