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, …, 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, …, 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 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 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 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 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] ⇒ 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] ⇒ A = 5, B = 2. 
import sys
from collections import deque

n, q = map(int, (sys.stdin.readline().split())) # number of elements in the deque and number of queries
if q == 0:
    sys.exit()
d = deque(map(int, (sys.stdin.readline().split()))) # the deque

queries = [(int(line.strip()), i) for (i, line) in enumerate(sys.stdin.readlines())]
queries.sort(reverse=True)
answers = [None] * q

# maybe it's a good idea to first sort the queries, so that we don't have to do the shuffling multiple times, but at most 1 time
# however, we need to remember how the queries were sorted

# probably a better idea to keep a separate from the deque,
# because it has to be popped every time

#debug print(queries)

curquery = queries.pop()
a = d.popleft()
#debug print(d)
for i in range(0,n):
    b = d.popleft()
    while i + 1 == curquery[0]: # we are going to do the (i+1)-th query now; so store any necessary results
        answers[curquery[1]] = (a, b)
        if(bool(queries)):
            curquery = queries.pop()
        else:
            break
    # now do the shuffle
    if a > b:
        d.append(b)
    else:
        d.append(a)
        a = b
    #debug print(f'{a}, {d}')

# after n operations, we know that a is the largest element
# so we can simply calculate all the others by shuffling
if curquery[0] > n:
    # then it has not been deal with yet, so put it with the remaining queries
    queries.append(curquery)
#debug print(f'Remaining queries: {queries}. Value of a: {a}')
for curquery in queries:
    answers[curquery[1]] = (a, d[(curquery[0] - 2) % (n - 1)])

for ans in answers:
    print(f'{ans[0]} {ans[1]}')
