{"trustable":false,"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":"\u003cp\u003eYou want to know if an integer number \u003cspan class\u003d\"tex2jax_process\"\u003e$N$\u003c/span\u003ecan be written as the sum of at least two consecutive natural numbers. For example:\u003c/p\u003e \n\u003cul class\u003d\"itemize\"\u003e \n \u003cli\u003e \u003cp\u003e\u003cspan class\u003d\"tex2jax_process\"\u003e$6 \u003d 1 + 2 + 3$\u003c/span\u003e\u003c/p\u003e \u003c/li\u003e \n \u003cli\u003e \u003cp\u003e\u003cspan class\u003d\"tex2jax_process\"\u003e$30 \u003d 9 + 10 + 11$\u003c/span\u003e\u003c/p\u003e \u003c/li\u003e \n\u003c/ul\u003e \n\u003cp\u003eIf we can find multiple solutions for a specific input, output the one with the smallest possible number of natural numbers that are summed.\u003c/p\u003e \n\u003ch2\u003eInput\u003c/h2\u003e \n\u003cp\u003eIn the first line of input you will find the number of test cases \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). Then follow the test cases.\u003c/p\u003e \n\u003cp\u003eEach test case consists of one line with a single integer number \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\u003ch2\u003eOutput\u003c/h2\u003e \n\u003cp\u003eFor each test case, output a single line containing a equation with the input number \u003cspan class\u003d\"tex2jax_process\"\u003e$N$\u003c/span\u003e for that case and the sum you have found. The format is as follows\u003cspan class\u003d\"tex2jax_process\"\u003e$N \u003d a + (a+1) + \\ldots + b$\u003c/span\u003e, as also shown in the example below. If there is no solution, output the word \u003ctt class\u003d\"ttfamily\"\u003eIMPOSSIBLE\u003c/tt\u003e.\u003c/p\u003e \n\u003ctable class\u003d\"sample\" summary\u003d\"sample data\"\u003e \n \u003ctbody\u003e\n \u003ctr\u003e \n \u003cth\u003eSample Input 1\u003c/th\u003e \n \u003cth\u003eSample Output 1\u003c/th\u003e \n \u003c/tr\u003e \n \u003ctr\u003e \n \u003ctd\u003e \u003cpre\u003e3\n8\n6\n30\n\u003c/pre\u003e \u003c/td\u003e \n \u003ctd\u003e \u003cpre\u003eIMPOSSIBLE\n6 \u003d 1 + 2 + 3\n30 \u003d 9 + 10 + 11\n\u003c/pre\u003e \u003c/td\u003e \n \u003c/tr\u003e \n \u003c/tbody\u003e\n\u003c/table\u003e"}}]}