You are considering a permutation ~P~ of ~0~ to ~N-1~ and a non-negative integer ~C~. The elements at indices ~i~ and ~j~ may be swapped only if ~P_i \oplus P_j \le C~ where ~A \oplus B~ denotes the XOR of ~A~ and ~B~. However, ~C~ has not yet been decided. What is the smallest possible non-negative integer ~C~ so that this permutation may be sorted from least to greatest?

To make this more interesting, the permutation will be updated. You are given ~Q~ updates of the form u v meaning that ~P_u~ and ~P_v~ have been swapped. After each of the ~Q~ updates, what is the best ~C~?

Note that the indices are 1-indexed, but the values are from ~0~ to ~N-1~.

Constraints

For all ~1 \le i \le N~, ~0 \le P_i \le N-1~.
~P~ is a permutation, so each element from ~0~ to ~N-1~ will appear exactly once.
~1 \le u, v \le N~

Subtask 1 [20%]

~1 \le N \le 400~
~1 \le Q \le 400~

Subtask 2 [30%]

~1 \le N \le 200\,000~
~Q = 1~

Subtask 3 [30%]

~1 \le N \le 50\,000~
~1 \le Q \le 50\,000~

Subtask 4 [20%]

~1 \le N \le 200\,000~
~1 \le Q \le 200\,000~

Input Specification

The first line will contain two space-separated integers, ~N~ and ~Q~.
The next line will contain ~N~ space-separated integers, ~P_1, P_2, \dots, P_N~.
The following ~Q~ lines will each contain two space-separated integers, ~u~ and ~v~, the indices to be swapped.

Output Specification

For each query, output a line containing a single non-negative integer, the smallest possible ~C~ given the current permutation.

Sample Input 1

4 2
2 3 1 0
4 3
1 1

Sample Output 1

2
2

Explanation for Sample 1

After the first update, the permutation is ~2, 3, 0, 1~. Swap ~2~ and ~0~, then ~3~ and ~1~.
The second update doesn't change anything.

Sample Input 2

4 3
1 0 2 3
1 2
3 4
1 4

Sample Output 2

0
1
2