레이팅 미적용Bethany 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 (\(w - 2\)) · (\(l - 2\)) 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.
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 \(w\), \(l\) (\(3 \le w\), \(l \le 10^{9}\)) — the dimensions of the bathroom.
For each test case, print an integer \(k\) (\(0 \le k\)) — the number of valid values of \(a\) for the given test case — followed by \(k\) integers \(a_{1}\), \(a_{2}\), . . . , \(a_{k}\) (\(1 \le a_{i}\)) — the valid values of \(a\). The values \(a_{1}\), \(a_{2}\), . . . , \(a_{k}\) 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