Problems
Maximal XOR
Maximal XOR
Given array of integers a_1, a_2, ..., a_n. For the given value of x find such a_i that x~xor~a_i is maximum.
Input data
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 data
For each value of x print in a separate line such value a_i that x~xor~a_i is maximum.
Examples
Input example #1
5 6 5 3 7 2 6 1 2 4 5 3 6
Output example #1
6 5 3 2 5 3