{"trustable":false,"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":"Alice has created a tree with $n$ nodes. Alice performed $m$ operations on the tree. Initially, every edge has 0 written on it. Operation $i$ can be described as - add $1$ to every edge in the path from node $a_i$ to node $b_i$.\n\u003cbr\u003e\nAfter all operations are performed, Alice checked that every edge has even number written on it. But, now Alice is confused. He may made a mistake in making the tree or executing the given operations.\n\nYour task is to determine whether there exists a tree with $n$ nodes, for which even number will be written on every edge after executing all the operations. \n"}},{"title":"Constraints","value":{"format":"HTML","content":"\u003csection\u003e\n \u003cul\u003e\n \u003cli\u003e\u003cvar\u003e\\(2 ≤ n ≤ 10^5\\)\u003c/var\u003e\u003c/li\u003e\n \u003cli\u003e\u003cvar\u003e\\(1 ≤ m ≤ 10^5\\)\u003c/var\u003e\u003c/li\u003e\n \u003cli\u003e\u003cvar\u003e\\(1 ≤ a_i,b_i ≤ n\\)\u003c/var\u003e\u003c/li\u003e\n \u003cli\u003e\u003cvar\u003e\\(a_i ≠ b_i\\)\u003c/var\u003e\u003c/li\u003e\n \u003c/ul\u003e\n\u003c/section\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003csection\u003e\n \u003cp\u003eInput is given as follows:\u003c/p\u003e\n \u003cpre\u003e\u003cvar\u003e\\(n\\)\u003c/var\u003e \u003cvar\u003e\\(m\\)\u003c/var\u003e\n\u003cvar\u003e\\(a_1\\)\u003c/var\u003e \u003cvar\u003e\\(b_1\\)\u003c/var\u003e\n:\n\u003cvar\u003e\\(a_M\\)\u003c/var\u003e \u003cvar\u003e\\(b_M\\)\u003c/var\u003e\n\u003c/pre\u003e\n\u003c/section\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003csection\u003e\n \u003cp\u003eOutput \u003ccode\u003eYES\u003c/code\u003e if there exists a tree, output \u003ccode\u003eNO\u003c/code\u003e otherwise.\u003c/p\u003e\n\u003c/section\u003e"}},{"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\n1 2\n2 4\n1 3\n3 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eYES\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003csection\u003e\n\u003c/section\u003e\u003csection\u003e\n \u003cp\u003ePossible tree 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.\u003c/p\u003e\n\u003c/section\u003e"}},{"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\n1 2\n3 5\n5 1\n3 4\n2 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eNO\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003csection\u003e\n\u003c/section\u003e\u003csection\u003e\n\u003c/section\u003e"}}]}