{"raw_statement":[{"iden":"problem statement","content":"There are $2N$ integers $A_1, A_2, ..., A_{2N}$ written on a blackboard, and an integer $M$ at least $2$.  \nAlice and Bob will play a game. They will alternately perform the following operation, with Alice going first, until there is no number on the blackboard.\n\n*   Choose a number and delete it from the blackboard.\n\nAt the end of the game, if the sum of numbers deleted by Alice modulo $M$ equals the sum of numbers deleted by Bob modulo $M$, Bob wins; otherwise, Alice wins.  \nWhich player will win if both plays optimally?"},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $2 \\leq M \\leq 10^9$\n*   $0 \\leq A_i \\leq M - 1$\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $M$\n$A_1$ $A_2$ $\\dots$ $A_{2N}$"},{"iden":"sample input 1","content":"2 9\n1 4 8 5"},{"iden":"sample output 1","content":"Alice\n\nThe game may proceed as follows.\n\n*   Alice deletes $1$.\n*   Bob deletes $4$.\n*   Alice deletes $5$.\n*   Bob deletes $8$.\n\nIn this case, the sum of numbers deleted by Alice modulo $M$ is $(1 + 5) \\bmod 9 = 6$, and the sum of numbers deleted by Bob modulo $M$ is $(4 + 8) \\bmod 9 = 3$. Since $6 \\neq 3$, Alice wins."},{"iden":"sample input 2","content":"3 998244353\n1 2 3 1 2 3"},{"iden":"sample output 2","content":"Bob"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}