{"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\u003eA tree is a connected undirected graph consisting of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e vertices and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e - 1\u003c/span\u003e edges. Vertices are numbered \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e through \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eLimak is a little polar bear and Radewoosh is his evil enemy. Limak once had a tree but Radewoosh stolen it. Bear is very sad now because he doesn\u0027t remember much about the tree\u0026nbsp;— he can tell you only three values \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eh\u003c/i\u003e\u003c/span\u003e:\u003c/p\u003e\u003cul\u003e \u003cli\u003e The tree had exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e vertices. \u003c/li\u003e\u003cli\u003e The tree had diameter \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e\u003c/span\u003e. In other words, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e\u003c/span\u003e was the biggest distance between two vertices. \u003c/li\u003e\u003cli\u003e Limak also remembers that he once rooted the tree in vertex \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e and after that its height was \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eh\u003c/i\u003e\u003c/span\u003e. In other words, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eh\u003c/i\u003e\u003c/span\u003e was the biggest distance between vertex \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e and some other vertex. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe distance between two vertices of the tree is the number of edges on the simple path between them.\u003c/p\u003e\u003cp\u003eHelp Limak to restore his tree. Check whether there exists a tree satisfying the given conditions. Find any such tree and print its edges in any order. It\u0027s also possible that Limak made a mistake and there is no suitable tree\u0026nbsp;– in this case print \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e-1\u003c/span\u003e\".\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains three integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eh\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e2 ≤ \u003ci\u003en\u003c/i\u003e ≤ 100 000, 1 ≤ \u003ci\u003eh\u003c/i\u003e ≤ \u003ci\u003ed\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e - 1\u003c/span\u003e)\u0026nbsp;— the number of vertices, diameter, and height after rooting in vertex \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e, respectively.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIf there is no tree matching what Limak remembers, print the only line with \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e-1\u003c/span\u003e\" (without the quotes).\u003c/p\u003e\u003cp\u003eOtherwise, describe any tree matching Limak\u0027s description. Print \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e - 1\u003c/span\u003e lines, each with two space-separated integers\u0026nbsp;– indices of vertices connected by an edge. If there are many valid trees, print any of them. You can print edges in any order.\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\u003e5 3 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1 2\n1 3\n3 4\n3 5\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\u003e8 5 2\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\u003e8 4 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4 8\n5 7\n2 3\n8 1\n2 1\n5 6\n1 5\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\u003eBelow you can see trees printed to the output in the first sample and the third sample.\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/a48a9777fdfab70966911d8d356a39aa?v\u003d1715833486\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e"}}]}