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 java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public final class Code
{
	public static void main (String[] args) throws java.lang.Exception
	{   Scanner  sc=new Scanner(System.in);
	    int n=sc.nextInt();int q=sc.nextInt(),idx=0;
	    long m,m1,d,max=-1,x,y;
	    ArrayList<Long> a=new ArrayList<Long>();
	    for(int i=0;i<n;i++)
	    {    d=sc.nextLong();
	         if(d>max)
	         {  max=d;
	            idx=i;
	         }
	         a.add(d);
	    }
	    long d1[]=new long[idx];
	    long d2[]=new long[idx];
	    for(int i=0;i<idx;i++)
	    {   x=a.get(0);
	        y=a.get(1);
	        d1[i]=x;d2[i]=y;
	        if(x>y)
	        {   a.remove(1);
	            a.add(y);
	        }
	        else
	        {   a.remove(0);
	            a.add(x);
	        }
	    }
	    a.remove(0);
	    for(int i=0;i<q;i++)
	    {   m=sc.nextLong();
	        m=m-1;
	        m1=m-idx;
	        if(m1>=0)
	        {   int z=(int)(m1%(n-1)); 
	            System.out.println(max+" "+a.get(z));
	        }
	        else
	            System.out.println(d1[(int)m]+" "+d2[(int)m]);
	    }
	}
}
