{"raw_statement":[{"iden":"background","content":"# statement updated:\n$z$ is the number of numbers whose values are $0$."},{"iden":"statement","content":"Alice and Bob are playing a game against each other.\n\nIn front of them are a multiset $\\{a_i\\}$ of non-negative integers and a single integer $x$. Each number in $a$ is $0$ or $2^i(0\\le i<k)$ before the game.\n\nThis game will be a turn-based game, and Alice will go first. In one person's turn, he or she will choose an integer from $a$. Let this number be $p$. Then this person will choose whether or not to make $x\\gets x\\oplus p$, then remove $p$ from $a$. Here, operation $\\oplus$ means bitwise xor.\n\nAlice wants to make $x$ as big as possible, and Bob wants to make $x$ as small as possible.\n\nYou are a bystander who wants to know the final value of $x$. However, the size of $a$ is a huge number. Formally, there are $b_i$ numbers whose values are $2^i$ in $a$ for all $0\\le i<k$, and $z$ numbers whose values are $0$. But you still want to challenge this impossible problem.\n\nIf Alice and Bob are smart enough, please output the final value of $x$."},{"iden":"input","content":"The first line contains two integers $k,z(1\\le k\\le10^5,0\\le z\\le 10^9)$.\n\nThe next line contains $k$ integers, the $i$ -th integer is $b_{i-1}(0\\le b_{i-1}\\le10^9)$."},{"iden":"output","content":"Output the answer in binary format. Note that you should output exactly $k$ digit from high to low even though this number has leading $0$s."}],"translated_statement":null,"sample_group":[["1 0\n3","1"],["2 0\n2 1","11"],["2 0\n2 2","00"]],"show_order":[],"formal_statement":null,"simple_statement":null,"has_page_source":false}