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.io.*;
import java.util.*;
public class MainClass
{
    static int findmax(int a[])
    {
        int pos=0;
        for(int i=1;i<a.length;i++)
        {
            if(Math.abs(a[i])>Math.abs(a[pos]))
            pos=i;
        }
        return pos;
    }
	public static void main(String args[])throws IOException
	{
	    try
	    {
    		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    		String t_input[];
            t_input=br.readLine().split(" ");
            int n=Integer.parseInt(t_input[0]);
            int q=Integer.parseInt(t_input[1]);
            int ar[]=new int[n];
            t_input=br.readLine().split(" ");
            Deque<Integer> deque = new LinkedList<Integer>(); 
            for(int i=0;i<n;i++)
            {
                ar[i]=Integer.parseInt(t_input[i]);
                deque.addLast(ar[i]);
            }
            int x,y,a=0,b=0;
            int ar2[][]=new int[n+1][2];
            for(int i=1;i<n;i++)
            {
                x=deque.removeFirst();
                y=deque.removeFirst();
                if(x>y){a=x;b=y;}
                else{a=y;b=x;}
                //System.out.println(x+" xx "+y);
                ar2[i][0]=x;
                ar2[i][1]=y;
                deque.addFirst(a);
                deque.addLast(b);
            }
            int ar3[][]=new int[n+1][2];
            for(int i=1;i<n;i++)
            {
                x=deque.removeFirst();
                y=deque.removeFirst();
                //System.out.println(x+" xx "+y);
                if(x>y){a=x;b=y;}
                else{a=y;b=x;}
                ar3[i][0]=x;
                ar3[i][1]=y;
                //System.out.println(a+" "+b);
                deque.addFirst(a);
                deque.addLast(b);
            }
            long m;
            for(int i=0;i<q;i++)
            {
                m=Long.parseLong(br.readLine());
                int code=(int)(m%(n-1));
                if(code==0)
                code=n-1;
                if(m<n)
                System.out.println(ar2[(int)m][0]+" "+ar2[(int)m][1]);
                else
                System.out.println(ar3[code][0]+" "+ar3[code][1]);
            }
           // System.out.println(a+" "+b);
	    }
		catch(NumberFormatException x){}
	}
}
/*
__________TEST INPUT:
int test=Integer.parseInt(br.readLine());
    	    
__________n INPUT:
int n=Integer.parseInt(br.readLine());
    		
__________ARRAY INPUT:
String a_input[];
        a_input=br.readLine().split(" ");
        int a[]=new int[n];
        for(int i=0;i<n;i++)
        {
            a[i]=Integer.parseInt(a_input[i]);
        }

__________INPUT FOR TWO SPACE SEPARATED INTEGERS:
String t_input[];
t_input=br.readLine().split(" ");
int n=Integer.parseInt(t_input[0]);
int k=Integer.parseInt(t_input[1]);

__________STRING TO INTEGER ARRAY: ex-12345 to 1,2,3,4,5
String st=br.readLine();
char chars[]=st.toCharArray();
int a[]=new int[st.length()];
for(int i=0;i<st.length();i++)
a[i]=chars[i]-48;

__________ARRAY WITH SPACE SEPARATED INTEGERS:
int a[]=new int[n];
	        String t_input[];
            t_input=br.readLine().split(" ");
            for(int i=0;i<n;i++)
            {
                int a[i]=Integer.parseInt(t_input[i]);
            }

__________TO SORT IN DESCENDING: Arrays.sort(b,Collections.reverseOrder());
*/

