{"raw_statement":[{"iden":"problem statement","content":"For strings $s$ and $t$, we will say that $s$ and $t$ are _prefix-free_ when neither is a prefix of the other.\nLet $L$ be a positive integer. A set of strings $S$ is a _good string set_ when the following conditions hold true:\n\n*   Each string in $S$ has a length between $1$ and $L$ (inclusive) and consists of the characters `0` and `1`.\n*   Any two distinct strings in $S$ are prefix-free.\n\nWe have a good string set $S = { s_1, s_2, ..., s_N }$. Alice and Bob will play a game against each other. They will alternately perform the following operation, starting from Alice:\n\n*   Add a new string to $S$. After addition, $S$ must still be a good string set.\n\nThe first player who becomes unable to perform the operation loses the game. Determine the winner of the game when both players play optimally."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 10^5$\n*   $1 \\leq L \\leq 10^{18}$\n*   $s_1$, $s_2$, ..., $s_N$ are all distinct.\n*   { $s_1$, $s_2$, ..., $s_N$ } is a good string set.\n*   $|s_1| + |s_2| + ... + |s_N| \\leq 10^5$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $L$\n$s_1$\n$s_2$\n$:$\n$s_N$"},{"iden":"sample input 1","content":"2 2\n00\n01"},{"iden":"sample output 1","content":"Alice\n\nIf Alice adds `1`, Bob will be unable to add a new string."},{"iden":"sample input 2","content":"2 2\n00\n11"},{"iden":"sample output 2","content":"Bob\n\nThere are two strings that Alice can add on the first turn: `01` and `10`. In case she adds `01`, if Bob add `10`, she will be unable to add a new string. Also, in case she adds `10`, if Bob add `01`, she will be unable to add a new string."},{"iden":"sample input 3","content":"3 3\n0\n10\n110"},{"iden":"sample output 3","content":"Alice\n\nIf Alice adds `111`, Bob will be unable to add a new string."},{"iden":"sample input 4","content":"2 1\n0\n1"},{"iden":"sample output 4","content":"Bob\n\nAlice is unable to add a new string on the first turn."},{"iden":"sample input 5","content":"1 2\n11"},{"iden":"sample output 5","content":"Alice"},{"iden":"sample input 6","content":"2 3\n101\n11"},{"iden":"sample output 6","content":"Bob"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}