25062번 - Boundary 다국어

문제

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ドル × 1$ centimeters, she would use $w · l$ of them.

However, she has something different in mind.

• On the interior of the floor she wants to use the 1ドル × 1$ tiles. She needs exactly $(w - 2) · (l - 2)$ of these.
• On the floor boundary she wants to use tiles of size 1ドル × a$ for some positive integer $a$. The tiles can also be rotated by 90ドル$ degrees.

For which values of $a$ can Bethany tile the bathroom floor as described? Note that $a$ can also be 1ドル$.

입력

Each test contains multiple test cases. The first line contains an integer $t$ (1ドル ≤ t ≤ 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,ドル $l$ (3ドル ≤ w, l ≤ 10^9$) — the dimensions of the bathroom.

출력

For each test case, print an integer $k$ (0ドル ≤ k$) — the number of valid values of $a$ for the given test case — followed by $k$ integers $a_1,ドル $a_2,ドル $\dots,ドル $a_k$ (1ドル ≤ a_i$) — the valid values of $a$. The values $a_1,ドル $a_2,ドル $\dots,ドル $a_k$ have to be sorted from smallest to largest.

It is guaranteed that under the problem constraints, the output contains at most 200ドル,000円$ integers.

제한

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