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Problems

Maximal XOR

Maximal XOR

Time limit 1 second
Memory limit 256 MiB

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