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 \(1\).
Output
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.
Note
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.
Примеры
| № | Входные данные | Выходные данные |
|
1
|
3
3 5
12 12
314159265 358979323
|
3 1 2 3
3 1 2 11
2 1 2
|