Maximal XOR — Eolymp

Input

The first line contains the numbers $n$ $(n \leq 1 0^{5})$ (n \le 10^5) and $q$ . The second line contains integers $a_{1}, a_{2}, \dots, a_{n}$ a_1, a_2, \ldots, a_n $(0 \leq a_{i} \leq 1 0^{18})$ (0 \le a_i \le 10^{18}). Each of the next $q$ lines contains one number $x$ $(0 \leq x \leq 1 0^{18})$ (0 \le x \le 10^{18}).

Output

For each value of $x$ , print in a separate line such a value $a_{i}$ a_i that $x xor a_{i}$ x \mathbin{\mathrm{xor}} a_i is maximized.

Examples

Example 1

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