{"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\u003eThe Republic of AtCoder has \u003cvar\u003e\\(N\\)\u003c/var\u003e cities and \u003cvar\u003e\\(M\\)\u003c/var\u003e roads.\u003c/p\u003e\r\n\u003cp\u003eThe cities are numbered \u003cvar\u003e\\(1\\)\u003c/var\u003e through \u003cvar\u003e\\(N\\)\u003c/var\u003e, and the roads are numbered \u003cvar\u003e\\(1\\)\u003c/var\u003e through \u003cvar\u003e\\(M\\)\u003c/var\u003e. Road \u003cvar\u003e\\(i\\)\u003c/var\u003e connects City \u003cvar\u003e\\(A_i\\)\u003c/var\u003e and City \u003cvar\u003e\\(B_i\\)\u003c/var\u003e bidirectionally.\u003c/p\u003e\r\n\u003cp\u003eThere is a rush hour in the country that peaks at time \u003cvar\u003e\\(0\\)\u003c/var\u003e. If you start going through Road \u003cvar\u003e\\(i\\)\u003c/var\u003e at time \u003cvar\u003e\\(t\\)\u003c/var\u003e, it will take \u003cvar\u003e\\(C_i+ \\left\\lfloor \\frac{D_i}{t+1} \\right\\rfloor\\)\u003c/var\u003e time units to reach the other end. (\u003cvar\u003e\\(\\lfloor x\\rfloor\\)\u003c/var\u003e denotes the largest integer not exceeding \u003cvar\u003e\\(x\\)\u003c/var\u003e.)\u003c/p\u003e\r\n\u003cp\u003eTakahashi is planning to depart City \u003cvar\u003e\\(1\\)\u003c/var\u003e at time \u003cvar\u003e\\(0\\)\u003c/var\u003e or some \u003cstrong\u003einteger time\u003c/strong\u003e later and head to City \u003cvar\u003e\\(N\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003cp\u003ePrint the earliest time when Takahashi can reach City \u003cvar\u003e\\(N\\)\u003c/var\u003e if he can stay in each city for an \u003cstrong\u003einteger number of time units\u003c/strong\u003e. It can be proved that the answer is an integer under the Constraints of this problem.\u003c/p\u003e\r\n\u003cp\u003eIf City \u003cvar\u003e\\(N\\)\u003c/var\u003e is unreachable, print \u003ccode\u003e-1\u003c/code\u003e instead.\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 \\leq N \\leq 10^5\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(0 \\leq M \\leq 10^5\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 \\leq A_i,B_i \\leq N\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(0 \\leq C_i,D_i \\leq 10^9\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003eAll values in input are integers.\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 \u003cvar\u003e\\(C_1\\)\u003c/var\u003e \u003cvar\u003e\\(D_1\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(\\vdots\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(A_M\\)\u003c/var\u003e \u003cvar\u003e\\(B_M\\)\u003c/var\u003e \u003cvar\u003e\\(C_M\\)\u003c/var\u003e \u003cvar\u003e\\(D_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 an integer representing the earliest time when Takahashi can reach City \u003cvar\u003e\\(N\\)\u003c/var\u003e, or \u003ccode\u003e-1\u003c/code\u003e if City \u003cvar\u003e\\(N\\)\u003c/var\u003e is unreachable.\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\u003e2 1\r\n1 2 2 3\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4\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\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\u003cp\u003eWe will first stay in City \u003cvar\u003e\\(1\\)\u003c/var\u003e until time \u003cvar\u003e\\(1\\)\u003c/var\u003e. Then, at time \u003cvar\u003e\\(1\\)\u003c/var\u003e, we will start going through Road \u003cvar\u003e\\(1\\)\u003c/var\u003e, which will take \u003cvar\u003e\\(2+\\left\\lfloor \\frac{3}{1+1} \\right\\rfloor \u003d 3\\)\u003c/var\u003e time units before reaching City \u003cvar\u003e\\(2\\)\u003c/var\u003e at time \u003cvar\u003e\\(4\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003cp\u003eIt is impossible to reach City \u003cvar\u003e\\(2\\)\u003c/var\u003e earlier than time \u003cvar\u003e\\(4\\)\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\u003e2 3\r\n1 2 2 3\r\n1 2 2 1\r\n1 1 1 1\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\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\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\u003cp\u003eThere may be multiple roads connecting the same pair of cities, and a road going from a city to the same city.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 3","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 2\r\n1 2 3 4\r\n3 4 5 6\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e-1\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\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\u003cp\u003eThere may be no path from City \u003cvar\u003e\\(1\\)\u003c/var\u003e to City \u003cvar\u003e\\(N\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 4","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\u003e6 9\r\n1 1 0 0\r\n1 3 1 2\r\n1 5 2 3\r\n5 2 16 5\r\n2 6 1 10\r\n3 4 3 4\r\n3 5 3 10\r\n5 6 1 100\r\n4 2 0 110\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e20\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\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\u003c/section\u003e\r\n"}}]}