A. Valeriy and Deque
time limit per test
6 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with $$$n$$$ elements. The $$$i$$$-th element is $$$a_i$$$ ($$$i$$$ = $$$1, 2, \ldots, n$$$). He gradually takes the first two leftmost elements from the deque (let's call them $$$A$$$ and $$$B$$$, respectively), and then does the following: if $$$A > B$$$, he writes $$$A$$$ to the beginning and writes $$$B$$$ to the end of the deque, otherwise, he writes to the beginning $$$B$$$, and $$$A$$$ writes to the end of the deque. We call this sequence of actions an operation.

For example, if deque was $$$[2, 3, 4, 5, 1]$$$, on the operation he will write $$$B=3$$$ to the beginning and $$$A=2$$$ to the end, so he will get $$$[3, 4, 5, 1, 2]$$$.

The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him $$$q$$$ queries. Each query consists of the singular number $$$m_j$$$ $$$(j = 1, 2, \ldots, q)$$$. It is required for each query to answer which two elements he will pull out on the $$$m_j$$$-th operation.

Note that the queries are independent and for each query the numbers $$$A$$$ and $$$B$$$ should be printed in the order in which they will be pulled out of the deque.

Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.

Input

The first line contains two integers $$$n$$$ and $$$q$$$ ($$$2 \leq n \leq 10^5$$$, $$$0 \leq q \leq 3 \cdot 10^5$$$) — the number of elements in the deque and the number of queries. The second line contains $$$n$$$ integers $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$, where $$$a_i$$$ $$$(0 \leq a_i \leq 10^9)$$$ — the deque element in $$$i$$$-th position. The next $$$q$$$ lines contain one number each, meaning $$$m_j$$$ ($$$1 \leq m_j \leq 10^{18}$$$).

Output

For each teacher's query, output two numbers $$$A$$$ and $$$B$$$ — the numbers that Valeriy pulls out of the deque for the $$$m_j$$$-th operation.

Examples
Input
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note
     Consider all 10 steps for the first test in detail:
  1.  $$$[1, 2, 3, 4, 5]$$$ — on the first operation, $$$A$$$ and $$$B$$$ are $$$1$$$ and $$$2$$$, respectively.
    So, $$$2$$$ we write to the beginning of the deque, and $$$1$$$ — to the end.
    We get the following status of the deque: $$$[2, 3, 4, 5, 1]$$$.
  2.  $$$[2, 3, 4, 5, 1] \Rightarrow A = 2, B = 3$$$.
  3.  $$$[3, 4, 5, 1, 2]$$$
  4.  $$$[4, 5, 1, 2, 3]$$$
  5.  $$$[5, 1, 2, 3, 4]$$$
  6.  $$$[5, 2, 3, 4, 1]$$$
  7.  $$$[5, 3, 4, 1, 2]$$$
  8.  $$$[5, 4, 1, 2, 3]$$$
  9.  $$$[5, 1, 2, 3, 4]$$$
  10.  $$$[5, 2, 3, 4, 1] \Rightarrow A = 5, B = 2$$$.