Maximal XOR

Given array of integers $a_1,a_2,...,a_n$. For the given value of $x$ find such $a_i$ that $xxor{a}_i$ is maximum.

Input

First line contains number $n(n\le 10^5)$ and number of queries $q$. Second line contains integers $a_1,a_2,...,a_n(0\le a_i\le 10^{18})$. Each of the next $q$ lines contains one number $x(0\le x\le 10^{18})$.

Output

For each value of $x$ print in a separate line such value $a_i$ that $xxor{a}_i$ is maximum.

Examples