408470: GYM103145 E Easy Math Problem

Kanari recently worked on perfect numbers.

Perfect numbers are a special kind of natural numbers. A number is a perfect number if and only if the sum of all the true factors (divisors other than itself) is equal to itself. Such as $$$6=1+2+3$$$, $$$28=1+2+4+7+14$$$, etc.

Kanari made a kind of semi-perfect number of his own according to the definition of perfect number.

Let $$$S$$$ be the set of all the true factors of the natural number $$$X$$$. If there is a subset of $$$S$$$ such that the sum of the numbers in the subset is equal to the number itself, the number is said to be semi-perfect.

Obviously, all perfect numbers are semiperfect numbers. In addition, there are some numbers that are not perfect, and they also belong to Kanari's semi-perfect numbers. For example, the true factors set of $$$24$$$ is $$$\{1,2,3,4,6,8,12\}$$$, we can select a subset $$$\{2,4,6,12\}$$$, meet that $$$24=2+4+6+12$$$. So $$$24$$$ can be called a semi-perfect number.

Kanari wants to know if he can find an integer $$$k$$$ which is a multiple of positive integer $$$p$$$, such that $$$k$$$ is a semi-perfect number.

Since Kanari is not good at math, he wants the $$$k$$$ not to be too large ($$$k\leq 2\times 10^{18}$$$), and the size of the subset is not larger than 1000. He wants you to give the subset you select.

This problem contains multiple test cases.

The first line contains a single integer $$$T$$$ ($$$1\leq T\leq 4000$$$) indicating the number of test cases.

Then $$$T$$$ cases follow, each of which contains a single interger $$$p$$$ ($$$1\leq p\leq 10^9$$$).

Output $$$2T$$$ lines.

For each test case, if there is some integer $$$k$$$ that satisfy the condition, output two space-separated integers on the first line, $$$k$$$ ($$$k\leq 2\times 10^{18}$$$) and $$$n$$$ ($$$1 \leq n \leq 1000$$$) (the size of the subset you select). Then output $$$n$$$ space-separated integers on the second line, the subset you select.

If you cannot find such $$$k$$$, output -1 on the first line, and an empty line on the second line.

Please don't output extra space at the end of each line.

2
6
1

48 5
2 4 6 12 24
12 4
1 2 3 6