{"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\u003eConsider the following boring game about removing nodes from a forest. Initially, the forest contains only one tree with \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eN\u003c/i\u003e\u003c/span\u003e nodes, and your initial score is \u003cspan class\u003d\"tex-span\"\u003e0\u003c/span\u003e. The game then goes as follows:\u003c/p\u003e\u003col\u003e \u003cli\u003e If the forest is empty, the game is finished. Otherwise, you choose one node from the current forest uniformly at random. \u003c/li\u003e\u003cli\u003e Your score increases by the size of the tree which your chosen node belongs to. \u003c/li\u003e\u003cli\u003e Remove your chosen node and all edges connected to this node. Then proceed to step\u0026nbsp;1. \u003c/li\u003e\u003c/ol\u003e\u003cp\u003ePlease calculate the expected value of your final score multiplied by \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eN\u003c/i\u003e!\u003c/span\u003e, modulo \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\u003eThe first line of input contains one integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eN\u003c/i\u003e\u003c/span\u003e indicating the number of nodes in the initial tree.\u003c/p\u003e\u003cp\u003eEach of the following \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eN\u003c/i\u003e - 1\u003c/span\u003e lines contains two integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ey\u003c/i\u003e\u003c/span\u003e, indicating that \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e-th node and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ey\u003c/i\u003e\u003c/span\u003e-th node are connected by an edge in the given tree. The nodes are numbered from \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eN\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e\u003cul\u003e \u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003eN\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e \u003c/li\u003e\u003cli\u003e \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ex\u003c/i\u003e, \u003ci\u003ey\u003c/i\u003e ≤ \u003ci\u003eN\u003c/i\u003e\u003c/span\u003e \u003c/li\u003e\u003cli\u003e the given graph is a tree \u003c/li\u003e\u003c/ul\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eOutput one number: the expected value of the final score of this boring game multiplied by \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eN\u003c/i\u003e!\u003c/span\u003e, modulo \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\u003e2\n1 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\u003e3\n1 2\n2 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e34\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}