{"trustable":true,"prependHtml":"\u003cstyle type\u003d\"text/css\"\u003e\n section pre {\n display: block;\n padding: 9.5px;\n margin: 0 0 10px;\n font-size: 13px;\n line-height: 1.42857143;\n word-break: break-all;\n word-wrap: break-word;\n color: #333;\n background: rgba(255, 255, 255, 0.5);\n border: 1px solid #ccc;\n border-radius: 6px;\n }\n\u003c/style\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027\\\\(\u0027, right: \u0027\\\\)\u0027, display: false},\n {left: \u0027\\\\[\u0027, right: \u0027\\\\]\u0027, display: true}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"Problem Statement","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eTakahashi is not good at problems about trees in programming contests, and Aoki is helping him practice.\u003c/p\u003e\r\n\u003cp\u003eFirst, Takahashi created a tree with \u003cvar\u003e\\(N\\)\u003c/var\u003e vertices numbered \u003cvar\u003e\\(1\\)\u003c/var\u003e through \u003cvar\u003e\\(N\\)\u003c/var\u003e, and wrote \u003cvar\u003e\\(0\\)\u003c/var\u003e at each edge.\u003c/p\u003e\r\n\u003cp\u003eThen, Aoki gave him \u003cvar\u003e\\(M\\)\u003c/var\u003e queries. The \u003cvar\u003e\\(i\\)\u003c/var\u003e-th of them is as follows:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eIncrement the number written at each edge along the path connecting vertices \u003cvar\u003e\\(a_i\\)\u003c/var\u003e and \u003cvar\u003e\\(b_i\\)\u003c/var\u003e, by one.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003eAfter Takahashi executed all of the queries, he told Aoki that, for every edge, the written number became an even number.\r\nHowever, Aoki forgot to confirm that the graph Takahashi created was actually a tree, and it is possible that Takahashi made a mistake in creating a tree or executing queries.\u003c/p\u003e\r\n\u003cp\u003eDetermine whether there exists a tree that has the property mentioned by Takahashi.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Constraints","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cul\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(2 ≤ N ≤ 10^5\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 ≤ M ≤ 10^5\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 ≤ a_i,b_i ≤ N\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(a_i ≠ b_i\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Input","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eInput is given from Standard Input in the following format:\u003c/p\u003e\r\n\u003cpre\u003e\u003cvar\u003e\\(N\\)\u003c/var\u003e \u003cvar\u003e\\(M\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(a_1\\)\u003c/var\u003e \u003cvar\u003e\\(b_1\\)\u003c/var\u003e\r\n:\r\n\u003cvar\u003e\\(a_M\\)\u003c/var\u003e \u003cvar\u003e\\(b_M\\)\u003c/var\u003e\r\n\u003c/pre\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Output","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003ePrint \u003ccode\u003eYES\u003c/code\u003e if there exists a tree that has the property mentioned by Takahashi; print \u003ccode\u003eNO\u003c/code\u003e otherwise.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 1","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 4\r\n1 2\r\n2 4\r\n1 3\r\n3 4\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eYES\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003cp\u003eFor example, Takahashi\u0027s graph has the property mentioned by him if it has the following edges: \u003cvar\u003e\\(1-2\\)\u003c/var\u003e, \u003cvar\u003e\\(1-3\\)\u003c/var\u003e and \u003cvar\u003e\\(1-4\\)\u003c/var\u003e.\r\nIn this case, the number written at every edge will become \u003cvar\u003e\\(2\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 2","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 5\r\n1 2\r\n3 5\r\n5 1\r\n3 4\r\n2 3\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eNO\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\u003c/section\u003e\r\n"}}]}