{"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\u003eI have an undirected graph consisting of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e nodes, numbered 1 through \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e. Each node has at most two incident edges. For each pair of nodes, there is at most an edge connecting them. No edge connects a node to itself.\u003c/p\u003e\u003cp\u003eI would like to create a new graph in such a way that: \u003c/p\u003e\u003cul\u003e \u003cli\u003e The new graph consists of the same number of nodes and edges as the old graph. \u003c/li\u003e\u003cli\u003e The properties in the first paragraph still hold. \u003c/li\u003e\u003cli\u003e For each two nodes \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e, if there is an edge connecting them in the old graph, there is no edge connecting them in the new graph. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eHelp me construct the new graph, or tell me if it is impossible.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line consists of two space-separated integers: \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003em\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e), denoting the number of nodes and edges, respectively. Then \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e lines follow. Each of the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e lines consists of two space-separated integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003eu\u003c/i\u003e, \u003ci\u003ev\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e;\u0026nbsp;\u003ci\u003eu\u003c/i\u003e ≠ \u003ci\u003ev\u003c/i\u003e\u003c/span\u003e), denoting an edge between nodes \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIf it is not possible to construct a new graph with the mentioned properties, output a single line consisting of -1. Otherwise, output exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e lines. Each line should contain a description of edge in the same way as used in the input format.\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\u003e8 7\n1 2\n2 3\n4 5\n5 6\n6 8\n8 7\n7 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1 4\n4 6\n1 6\n2 7\n7 5\n8 5\n2 8\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","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\u003e3 2\n1 2\n2 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e-1\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","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\u003e5 4\n1 2\n2 3\n3 4\n4 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1 3\n3 5\n5 2\n2 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eThe old graph of the first example:\u003c/p\u003e\u003cp\u003e\u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/b02a93b5868e996af436638f840cb56d?v\u003d1715922496\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u003c/p\u003e\u003cp\u003eA possible new graph for the first example:\u003c/p\u003e\u003cp\u003e\u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/a7dd2facc1bd34548920ab19fa0809a5?v\u003d1715922496\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u003c/p\u003e\u003cp\u003eIn the second example, we cannot create any new graph.\u003c/p\u003e\u003cp\u003eThe old graph of the third example:\u003c/p\u003e\u003cp\u003e\u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/4fdffc03104cd49f2574389ecb9c90b6?v\u003d1715922496\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u003c/p\u003e\u003cp\u003eA possible new graph for the third example:\u003c/p\u003e\u003cp\u003e\u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/213382d6acf904ab576efed4c4c8c75b?v\u003d1715922496\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u003c/p\u003e"}}]}