Mexor

You are given an array consisting of $n$ non-negative integers, and m queries. Each query is characterized by one number $x$ and consists of the following consecutive steps:

• Perform the bitwise addition operation modulo 2 (xor) of each array element with the number $x$;

• Find mex of the resulting array.

Note that after each query the array changes.

Input

First line contains two integer numbers $n$ and $m(1\le n,m\le 3\cdot 10^5)$ — number of elements in array and number of queries.

Next line contains $n$ integer numbers $a_i(0\le a_i\le 3\cdot 10^5)$ — elements of then array.

Each of next m lines contains query — one integer number $x(0\le x\le 3\cdot 10^5)$.

Output

For each query print the answer on a separate line.

Examples

Mex of a sequence of numbers is the minimum non-negative number that is not present in the sequence as element. For example, $mex([4,33,0,1,1,5])=2$ and $mex([1,2,3])=0$.