{"trustable":true,"prependHtml":"\u003cstyle type\u003d\"text/css\"\u003e\n div.illustration {\n float: right;\n padding-left: 20px;\n }\n div.illustration .illustration {\n width: 100%;\n border-radius: 4px;\n }\n pre {\n display: block;\n margin: 0 0 10px;\n font-size: 13px;\n line-height: 1.42857143;\n color: #333;\n word-break: break-all;\n word-wrap: break-word;\n }\n\u003c/style\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027\\\\[\u0027, right: \u0027\\\\]\u0027, display: true}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\n \u003cp\u003eGiven an integer \u003cspan class\u003d\"tex2jax_process\"\u003e$N$\u003c/span\u003e,\n express it as the sum of at least two consecutive positive\n integers. For example:\u003c/p\u003e\n\n \u003cul class\u003d\"itemize\"\u003e\n \u003cli\u003e\n \u003cp\u003e\u003cspan class\u003d\"tex2jax_process\"\u003e$10 \u003d 1 + 2 + 3 +\n 4$\u003c/span\u003e\u003c/p\u003e\n \u003c/li\u003e\n\n \u003cli\u003e\n \u003cp\u003e\u003cspan class\u003d\"tex2jax_process\"\u003e$24 \u003d 7 + 8 +\n 9$\u003c/span\u003e\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ul\u003e\n\n \u003cp\u003eIf there are multiple solutions, output the one with the\n smallest possible number of summands.\u003c/p\u003e\n\n \u003ch2\u003eInput\u003c/h2\u003e\n\n \u003cp\u003eThe first line of input contains the number of test cases\n \u003cspan class\u003d\"tex2jax_process\"\u003e$T$\u003c/span\u003e (\u003cspan class\u003d\"tex2jax_process\"\u003e$1 \\leq T \\leq 2\\, 000$\u003c/span\u003e). The\n descriptions of the test cases follow:\u003c/p\u003e\n\n \u003cp\u003eEach test case consists of one line containing an integer\n \u003cspan class\u003d\"tex2jax_process\"\u003e$N$\u003c/span\u003e (\u003cspan class\u003d\"tex2jax_process\"\u003e$1 \\leq N \\leq 10^9$\u003c/span\u003e).\u003c/p\u003e\n\n \u003ch2\u003eOutput\u003c/h2\u003e\n\n \u003cp\u003eFor each test case, output a single line containing the\n equation in the format \u003cspan class\u003d\"tex2jax_process\"\u003e$N \u003d a +\n (a+1) + \\ldots + b$\u003c/span\u003e as in the example. If there is no\n solution, output a single word \u003ctt class\u003d\"ttfamily\"\u003eIMPOSSIBLE\u003c/tt\u003e instead.\u003c/p\u003e\n\n \u003ch2\u003eSample 1\u003c/h2\u003e\u003cbody\u003e\u003ctable class\u003d\"vjudge_sample\"\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\u003e3\n8\n10\n24\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eIMPOSSIBLE\n10 \u003d 1 + 2 + 3 + 4\n24 \u003d 7 + 8 + 9\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/body\u003e\n "}}]}