{"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\u003eQuite recently a creative student Lesha had a lecture on trees. After the lecture Lesha was inspired and came up with the tree of his own which he called a \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e-tree.\u003c/p\u003e\u003cp\u003eA \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e-tree is an infinite rooted tree where:\u003c/p\u003e\u003cul\u003e \u003cli\u003e each vertex has exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e children; \u003c/li\u003e\u003cli\u003e each edge has some weight; \u003c/li\u003e\u003cli\u003e if we look at the edges that goes from some vertex to its children (exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e edges), then their weights will equal \u003cspan class\u003d\"tex-span\"\u003e1, 2, 3, ..., \u003ci\u003ek\u003c/i\u003e\u003c/span\u003e. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe picture below shows a part of a 3-tree.\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003ccenter\u003e\u003cp\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/d1ca949761093b5dc4299aa1105a5ed1?v\u003d1715624512\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003c/center\u003e As soon as Dima, a good friend of Lesha, found out about the tree, he immediately wondered: \"How many paths of total weight \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e (the sum of all weights of the edges in the path) are there, starting from the root of a \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e-tree and also containing at least one edge of weight at least \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e\u003c/span\u003e?\".\u003cp\u003eHelp Dima find an answer to his question. As the number of ways can be rather large, print it modulo \u003cspan class\u003d\"tex-span\"\u003e1000000007\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 7\u003c/span\u003e). \u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eA single line contains three space-separated integers: \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ed\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003en\u003c/i\u003e, \u003ci\u003ek\u003c/i\u003e ≤ 100;\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ed\u003c/i\u003e ≤ \u003ci\u003ek\u003c/i\u003e\u003c/span\u003e).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint a single integer — the answer to the problem modulo \u003cspan class\u003d\"tex-span\"\u003e1000000007\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 7\u003c/span\u003e). \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\u003e3 3 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\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 3 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\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\u003e4 3 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e6\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\u003e4 5 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e7\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}