1180_C. Valeriy and Deque
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. 
```python
import sys
n,q=list(map(int,input().split()))
a=list(map(int,input().split()))
mx1=max(a)
a1=[]
dp={}
for i in range(q):
    a1.append(int(input()))
if a1==[]:
    mx=0
else:
    mx=max(a1)

count=0
while(1):
    count+=1
    val1=a[0]
    val2=a[1]
    if val1==mx1:
        break
    if val1>val2:
        a.remove(val2)
        a.append(val2)
    else:
        a.remove(val1)
        a.append(val1)
    dp[count]=(val1,val2)
    
#print(a)
for x in a1:
    if x in dp:
        print(dp[x][0],dp[x][1]) 
    else:
        xx=(x-count)%(n-1)
        print(a[0],a[xx+1])







"""

12345   12
23451   23
34512   34
45123   45
51234   51
52341   52
53412   53
54123   54
51234   51









3 4 5 2 1

34521  34
45213  45


a=[5,2,1,3,4]
52134  52   xx=0   0,1 
51342  51   xx=1   0,2
53421  53   xx=2   0,3
54213  54   xx=3   0,4

52134  52   xx=4   0,1
51342  51
53421  53












"""
```