{"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\u003eFor a connected undirected weighted graph \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eG\u003c/i\u003e\u003c/span\u003e, MST (minimum spanning tree) is a subgraph of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eG\u003c/i\u003e\u003c/span\u003e that contains all of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eG\u003c/i\u003e\u003c/span\u003e\u0027s vertices, is a tree, and sum of its edges is minimum possible.\u003c/p\u003e\u003cp\u003eYou are given a graph \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eG\u003c/i\u003e\u003c/span\u003e. If you run a MST algorithm on graph it would give you only one MST and it causes other edges to become jealous. You are given some queries, each query contains a set of edges of graph \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eG\u003c/i\u003e\u003c/span\u003e, and you should determine whether there is a MST containing all these edges or not.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains two integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e2 ≤ \u003ci\u003en\u003c/i\u003e, \u003ci\u003em\u003c/i\u003e ≤ 5·10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e - 1 ≤ \u003ci\u003em\u003c/i\u003e\u003c/span\u003e)\u0026nbsp;— the number of vertices and edges in the graph and the number of queries.\u003c/p\u003e\u003cp\u003eThe \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th of the next \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e lines contains three integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ev\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eu\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≠ \u003ci\u003ev\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ew\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 5·10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e)\u0026nbsp;— the endpoints and weight of the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th edge. There can be more than one edges between two vertices. It\u0027s guaranteed that the given graph is connected.\u003c/p\u003e\u003cp\u003eThe next line contains a single integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eq\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003eq\u003c/i\u003e ≤ 5·10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e)\u0026nbsp;— the number of queries.\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eq\u003c/i\u003e\u003c/span\u003e lines follow, the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th of them contains the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th query. It starts with an integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ek\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ \u003ci\u003en\u003c/i\u003e - 1\u003c/span\u003e)\u0026nbsp;— the size of edges subset and continues with \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e distinct space-separated integers from \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e to \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e\u0026nbsp;— the indices of the edges. It is guaranteed that the sum of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e for \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ei\u003c/i\u003e ≤ \u003ci\u003eq\u003c/i\u003e\u003c/span\u003e does not exceed \u003cspan class\u003d\"tex-span\"\u003e5·10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each query you should print \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eYES\u003c/span\u003e\" (without quotes) if there\u0027s a MST containing these edges and \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eNO\u003c/span\u003e\" (of course without quotes again) otherwise.\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 7\n1 2 2\n1 3 2\n2 3 1\n2 4 1\n3 4 1\n3 5 2\n4 5 2\n4\n2 3 4\n3 3 4 5\n2 1 7\n2 1 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eYES\nNO\nYES\nNO\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\u003eThis is the graph of sample:\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" height\u003d\"302px\" src\u003d\"CDN_BASE_URL/1fa184ce6ecd15e12438851b99c933eb?v\u003d1718732974\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\" width\u003d\"378px\"\u003e \u003c/center\u003e\u003cp\u003eWeight of minimum spanning tree on this graph is \u003cspan class\u003d\"tex-span\"\u003e6\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eMST with edges \u003cspan class\u003d\"tex-span\"\u003e(1, 3, 4, 6)\u003c/span\u003e, contains all of edges from the first query, so answer on the first query is \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eYES\u003c/span\u003e\".\u003c/p\u003e\u003cp\u003eEdges from the second query form a cycle of length \u003cspan class\u003d\"tex-span\"\u003e3\u003c/span\u003e, so there is no spanning tree including these three edges. Thus, answer is \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eNO\u003c/span\u003e\".\u003c/p\u003e"}}]}