Given a 0-indexed list of $N$ non-negative integers, and $Q$ queries each consisting of one non-negative integer $x$, output the smallest index of the minimum value in the list after each number in the list is XOR'd with $x$ for each query. Queries are persistent. That is, any previous queries change the list directly and affect the current query's answer.

Input Specification

The first line will contain two space-separated integers, $N$ $(1\le N\le {10}^5)$, and $Q$ $(1\le Q\le {10}^5)$.

The second line will contain $N$ space-separated integers, $a_0,a_1,\dots ,a_{N-1}$ $(0\le a_i\le {10}^9)$.

The next $Q$ lines will each contain one integer $x$ $(0\le x\le {10}^9)$.

Output Specification

For each query, output the smallest index of the minimum value in the list after every number in the list has been XOR'd with $x$.

Constraints

For all subtasks:

$1\le N,Q\le {10}^5$

Subtask 1 [5/17]

$1\le N,Q\le {10}^4$

Subtask 2 [12/17]

No additional constraints.

Sample Input 1

8 4
2 15 8 1 6 2 16 8
0
2
10
7

Sample Output 1

3
0
2
1

Explanation for Sample Output 1

2 15 8 1 6 2 16 8

The array is unchanged after the first XOR operation. The minimum is simply 1 at index 3.

0 13 10 3 4 0 18 10

In this case, the first of the two zeroes is chosen (index 0).

10 7 0 9 14 10 24 0

The first occurrence of the minimum value (0) is at index 2.

13 0 7 14 9 13 31 7

The minimum value (0) is at index 1.

Sample Input 2

7 5
7 7 8 0 0 10 16
12
14
16
6
12

Sample Output 2

2
3
6
6
6