{"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\u003eFor strings \u003cvar\u003e\\(s\\)\u003c/var\u003e and \u003cvar\u003e\\(t\\)\u003c/var\u003e, we will say that \u003cvar\u003e\\(s\\)\u003c/var\u003e and \u003cvar\u003e\\(t\\)\u003c/var\u003e are \u003cem\u003eprefix-free\u003c/em\u003e when neither is a prefix of the other.\u003c/p\u003e\r\n\u003cp\u003eLet \u003cvar\u003e\\(L\\)\u003c/var\u003e be a positive integer. A set of strings \u003cvar\u003e\\(S\\)\u003c/var\u003e is a \u003cem\u003egood string set\u003c/em\u003e when the following conditions hold true:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eEach string in \u003cvar\u003e\\(S\\)\u003c/var\u003e has a length between \u003cvar\u003e\\(1\\)\u003c/var\u003e and \u003cvar\u003e\\(L\\)\u003c/var\u003e (inclusive) and consists of the characters \u003ccode\u003e0\u003c/code\u003e and \u003ccode\u003e1\u003c/code\u003e.\u003c/li\u003e\r\n\u003cli\u003eAny two distinct strings in \u003cvar\u003e\\(S\\)\u003c/var\u003e are prefix-free.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003eWe have a good string set \u003cvar\u003e\\(S \u003d \\{ s_1, s_2, ..., s_N \\}\\)\u003c/var\u003e. Alice and Bob will play a game against each other. They will alternately perform the following operation, starting from Alice:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eAdd a new string to \u003cvar\u003e\\(S\\)\u003c/var\u003e. After addition, \u003cvar\u003e\\(S\\)\u003c/var\u003e must still be a good string set.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003eThe first player who becomes unable to perform the operation loses the game. Determine the winner of the game when both players play optimally.\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\\(1 \\leq N \\leq 10^5\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 \\leq L \\leq 10^{18}\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(s_1\\)\u003c/var\u003e, \u003cvar\u003e\\(s_2\\)\u003c/var\u003e, ..., \u003cvar\u003e\\(s_N\\)\u003c/var\u003e are all distinct.\u003c/li\u003e\r\n\u003cli\u003e{ \u003cvar\u003e\\(s_1\\)\u003c/var\u003e, \u003cvar\u003e\\(s_2\\)\u003c/var\u003e, ..., \u003cvar\u003e\\(s_N\\)\u003c/var\u003e } is a good string set.\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(|s_1| + |s_2| + ... + |s_N| \\leq 10^5\\)\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\\(L\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(s_1\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(s_2\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(:\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(s_N\\)\u003c/var\u003e\r\n\u003c/pre\u003e\r\n\r\n\u003c/section\u003e\r\n"}},{"title":"Output","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eIf Alice will win, print \u003ccode\u003eAlice\u003c/code\u003e; if Bob will win, print \u003ccode\u003eBob\u003c/code\u003e.\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 2\r\n00\r\n01\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eAlice\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\u003eIf Alice adds \u003ccode\u003e1\u003c/code\u003e, Bob will be unable to add a new string.\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 2\r\n00\r\n11\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eBob\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\u003eThere are two strings that Alice can add on the first turn: \u003ccode\u003e01\u003c/code\u003e and \u003ccode\u003e10\u003c/code\u003e.\r\nIn case she adds \u003ccode\u003e01\u003c/code\u003e, if Bob add \u003ccode\u003e10\u003c/code\u003e, she will be unable to add a new string.\r\nAlso, in case she adds \u003ccode\u003e10\u003c/code\u003e, if Bob add \u003ccode\u003e01\u003c/code\u003e, she will be unable to add a new string.\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\u003e3 3\r\n0\r\n10\r\n110\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eAlice\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\u003eIf Alice adds \u003ccode\u003e111\u003c/code\u003e, Bob will be unable to add a new string.\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\u003e2 1\r\n0\r\n1\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eBob\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\u003eAlice is unable to add a new string on the first turn.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 5","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\u003e1 2\r\n11\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eAlice\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\u003c/section\u003e\r\n"}},{"title":"Sample 6","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\n101\r\n11\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eBob\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"}}]}