{"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\u003eAt the ruins of Wat Phra Si Sanphet (วดพระศรสรรเพชญ), one can find famous inscriptions that have only recently been decoded. Several numbers written using Thai numerals decorate these ruins.\u003c/p\u003e\u003cp\u003eA couple of years ago, the famous Peruvian researcher Renzo \"el intrépido\" Morales found out that most numbers found at the ruins are palindromic, that is, they represent the same number when read backwards. For instance, 171 is palindromic, whereas 17 is not.\u003c/p\u003e\u003cp\u003eIntrigued by the existence of non palidromic numbers as decorations in the ruins, Renzo found out that, while these numbers are not palindromic when represented in base\u0026nbsp;10 (which is the base used in the Thai numeral system), they are palindromic when represented in another base. For \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e \u0026gt; 0\u003c/span\u003e, the base-\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003c/span\u003e representation of a number\u0026nbsp;\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eN\u003c/i\u003e\u003c/span\u003e is the sequence \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/sub\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003em\u003c/i\u003e - 1\u003c/sub\u003e... \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e0\u003c/sub\u003e\u003c/span\u003e so that \u003cspan class\u003d\"tex-span\"\u003e0 ≤ \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ \u003ci\u003eb\u003c/i\u003e - 1\u003c/span\u003e for each \u003cspan class\u003d\"tex-span\"\u003e0 ≤ \u003ci\u003ei\u003c/i\u003e ≤ \u003ci\u003em\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/sub\u003e ≠ 0\u003c/span\u003e, and \u003c/p\u003e\u003ccenter class\u003d\"tex-equation\"\u003e\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/sub\u003e\u003ci\u003eb\u003c/i\u003e\u003csup class\u003d\"upper-index\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/sup\u003e + \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003em\u003c/i\u003e - 1\u003c/sub\u003e\u003ci\u003eb\u003c/i\u003e\u003csup class\u003d\"upper-index\"\u003e\u003ci\u003em\u003c/i\u003e - 1\u003c/sup\u003e + ... + \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e\u003ci\u003eb\u003c/i\u003e + \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e0\u003c/sub\u003e \u003d \u003ci\u003eN\u003c/i\u003e.\u003c/span\u003e\u003c/center\u003e For the previous example, the base-2 representation of\u0026nbsp;17 is\u0026nbsp;10001, which is palindromic.\u003cp\u003eTo validate his discovery, Renzo wants you to write a program that takes a number represented in base\u0026nbsp;10 and checks in which bases from\u0026nbsp;2 to\u0026nbsp;16 such number has a palindromic representation.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line has a single integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eT\u003c/i\u003e\u003c/span\u003e, the number of test cases.\u003c/p\u003e\u003cp\u003eEach test case has a single line with an integer\u0026nbsp;\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eN\u003c/i\u003e\u003c/span\u003e written in base\u0026nbsp;10.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each test case, print in a single line a space-separated list of integers, from\u0026nbsp;2 to\u0026nbsp;16 and in increasing order, of the bases for which the representation of\u0026nbsp;\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eN\u003c/i\u003e\u003c/span\u003e is palindromic. If \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eN\u003c/i\u003e\u003c/span\u003e does not have a palindromic representation for any of the bases from\u0026nbsp;2 to\u0026nbsp;16, print\u0026nbsp;\u003cspan class\u003d\"tex-font-style-tt\"\u003e-1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-font-style-bf\"\u003eLimits\u003c/span\u003e \u003c/p\u003e\u003cul\u003e \u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e0 ≤ \u003ci\u003eT\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e3\u003c/sup\u003e\u003c/span\u003e \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e0 ≤ \u003ci\u003eN\u003c/i\u003e \u0026lt; 2\u003csup class\u003d\"upper-index\"\u003e31\u003c/sup\u003e\u003c/span\u003e \u003c/li\u003e\u003c/ul\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\n17\n2570\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2 4 16\n4 16\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}