{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eAn algorithm master in graph theory would never endure any disconnected subgraph.\u003c/p\u003e\u003cp\u003eAn esthetician would only consider edge-induced subgraphs as necessary subgraphs.\u003c/p\u003e\u003cp\u003eAn OCD patient would always choose a subgraph from a given simple undirected graph randomly.\u003c/p\u003e\u003cp\u003eThose are why Picard asks you to calculate, for choosing four different edges from a given simple undirected graph with equal probability among all possible ways, the probability that the edge-induced subgraph formed by chosen edges is connected. Here we say a subset of edges in the graph together with all vertices that are endpoints of edges in the subset form an edge-induced subgraph.\u003c/p\u003e\u003cp\u003eTo avoid any precision issue, Picard denotes the probability as $$$p$$$ and the number of edges as $$$m$$$, and you should report the value $$$\\left(p \\cdot \\binom{m}{4}\\right) \\bmod (10^9 + 7)$$$. It is easy to show that $$$p \\cdot \\binom{m}{4}$$$ is an integer.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe input contains several test cases, and the first line contains a positive integer $$$T$$$ indicating the number of test cases which is up to $$$10$$$.\u003c/p\u003e\u003cp\u003eFor each test case, the first line contains two integers $$$n$$$ and $$$m$$$ indicating the numbers of vertices and edges in the given simple undirected graph respectively, where $$$4 \\leq n \\leq 10^5$$$ and $$$4 \\leq m \\leq 2 \\times 10^5$$$.\u003c/p\u003e\u003cp\u003eThe following $$$m$$$ lines describe all edges of the graph, the $$$i$$$-th line of which contains two integers $$$u$$$ and $$$v$$$ which represent an edge between the $$$u$$$-th vertex and the $$$v$$$-th vertex, where $$$1 \\leq u, v \\leq n$$$ and $$$u \\neq v$$$.\u003c/p\u003e\u003cp\u003eWe guarantee that the given graph contains no loops or multiple edges.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each test case, output a line containing an integer corresponding to the value $$$\\left(p \\cdot \\binom{m}{4}\\right) \\bmod (10^9 + 7)$$$, where $$$p$$$ indicates the probability which you are asked to calculate.\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\n4 4\n1 2\n2 3\n3 4\n4 1\n4 6\n1 2\n1 3\n1 4\n2 3\n2 4\n3 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\n15\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}