P10558 [ICPC 2024 Xi'an I] XOR Game

# statement updated: $z$ is the number of numbers whose values are $0$.

Alice and Bob are playing a game against each other. In 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

The first line contains two integers $k,z(1\le k\le10^5,0\le z\le 10^9)$. The next line contains $k$ integers, the $i$ -th integer is $b_{i-1}(0\le b_{i-1}\le10^9)$.

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.