{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eKanari recently worked on perfect numbers.\u003c/p\u003e\u003cp\u003ePerfect numbers are a special kind of natural numbers. A number is a perfect number if and only if the sum of all the true factors (divisors other than itself) is equal to itself. Such as $$$6\u003d1+2+3$$$, $$$28\u003d1+2+4+7+14$$$, etc.\u003c/p\u003e\u003cp\u003eKanari made a kind of semi-perfect number of his own according to the definition of perfect number.\u003c/p\u003e\u003cp\u003eLet $$$S$$$ be the set of all the true factors of the natural number $$$X$$$. If there is a subset of $$$S$$$ such that the sum of the numbers in the subset is equal to the number itself, the number is said to be semi-perfect.\u003c/p\u003e\u003cp\u003eObviously, all perfect numbers are semiperfect numbers. In addition, there are some numbers that are not perfect, and they also belong to Kanari\u0027s semi-perfect numbers. For example, the true factors set of $$$24$$$ is $$$\\{1,2,3,4,6,8,12\\}$$$, we can select a subset $$$\\{2,4,6,12\\}$$$, meet that $$$24\u003d2+4+6+12$$$. So $$$24$$$ can be called a semi-perfect number.\u003c/p\u003e\u003cp\u003eKanari wants to know if he can find an integer $$$k$$$ which is a multiple of positive integer $$$p$$$, such that $$$k$$$ is a semi-perfect number.\u003c/p\u003e\u003cp\u003eSince Kanari is not good at math, he wants the $$$k$$$ not to be too large ($$$k\\leq 2\\times 10^{18}$$$), and the size of the subset is not larger than 1000. He wants you to give the subset you select.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThis problem contains multiple test cases.\u003c/p\u003e\u003cp\u003eThe first line contains a single integer $$$T$$$ ($$$1\\leq T\\leq 4000$$$) indicating the number of test cases.\u003c/p\u003e\u003cp\u003eThen $$$T$$$ cases follow, each of which contains a single interger $$$p$$$ ($$$1\\leq p\\leq 10^9$$$).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eOutput $$$2T$$$ lines.\u003c/p\u003e\u003cp\u003eFor each test case, if there is some integer $$$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$$$ space-separated integers on the second line, the subset you select.\u003c/p\u003e\u003cp\u003eIf you cannot find such $$$k$$$, output \u003cspan class\u003d\"tex-font-style-tt\"\u003e-1\u003c/span\u003e on the first line, and an empty line on the second line.\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003ePlease don\u0027t output extra space at the end of each line.\u003c/span\u003e\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e2\n6\n1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e48 5\n2 4 6 12 24\n12 4\n1 2 3 6\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}