{"trustable":true,"prependHtml":"\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 async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eThere is a directed acyclic graph with $n$ vertices and $m$ edges. You are allowed to delete exact $k$ edges in such way that the lexicographically minimal topological sort of the graph is minimum possible.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"There are multiple test cases. The first line of input contains an integer $T$ indicating the number of test cases. For each test case:\u003cbr\u003e\u003cbr\u003eThe first line contains three integers $n$, $m$ and $k$ $(1 \\le n \\le 100000, 0 \\le k \\le m \\le 200000)$ -- the number of vertices, the number of edges and the number of edges to delete.\u003cbr\u003e\u003cbr\u003eFor the next $m$ lines, each line contains two integers $u_i$ and $v_i$, which means there is a directed edge from $u_i$ to $v_i$ $(1 \\le u_i, v_i \\le n)$.\u003cbr\u003e\u003cbr\u003eYou can assume the graph is always a dag. The sum of values of $n$ in all test cases doesn\u0027t exceed $10^6$. The sum of values of $m$ in all test cases doesn\u0027t exceed $2 \\times 10^6$."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, output an integer $S \u003d (\\displaystyle\\sum_{i\u003d1}^{n}{i\\cdot p_i}) \\text{ mod } (10^9 + 7)$, where $p_{1}, p_{2}, ..., p_{n}$ is the lexicographically minimal topological sort of the graph."}},{"title":"Sample","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\r\n4 2 0\r\n1 2\r\n1 3\r\n4 5 1\r\n2 1\r\n3 1\r\n4 1\r\n2 3\r\n2 4\r\n4 4 2\r\n1 2\r\n2 3\r\n3 4\r\n1 4\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e30\r\n27\r\n30\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}