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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

/* Name of the class has to be "Main" only if the class is public. */
public class signs
{ 
	private static class pair {
    int first;
    int second;

    public pair(int first, int second) {
        this.first = first;
        this.second = second;
    }

    public String toString() {
        final StringBuilder sb = new StringBuilder();
        sb.append(first).append(" ");
        sb.append(second);
        return sb.toString();
    }

}
	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;
		//it reads the data about the specified point and divide the data about it ,it is quite fast
		//than using direct 

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception r) {
					r.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());//converts string to integer
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception r) {
				r.printStackTrace();
			}
			return str;
		}
	}
	
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
    public static long power(long x,long y,int r) {
		if(y==0) {
			return 1;
		}if(y==1) {
			return x%r;
		}else if(y%2==0) {
			return power((x*x)%r,y/2,r);
		}else {
			return (x*power((x*x%r),y/2,r))%r;
		}
	}
	public static void main (String[] args) throws java.lang.Exception
	{
	   ArrayList<Integer>list=new ArrayList<Integer>();
	   
	   Scanner in=new Scanner(System.in);
		int n=in.nextInt();
		int q=in.nextInt();
		for(int i=0;i<n;i++)
		{
			list.add(in.nextInt());
		}
		int max=Collections.max(list);
		int t=list.indexOf(max);int p=0;int y=t;
		  signs.pair[] ans = new signs.pair[y+5];
		while(t-->0)
		{int f=list.get(0);int s=list.get(1);
			ans[p]=new signs.pair(f, s);p++;
			if(f>s)
			{
				list.remove(1);
				list.add(s);
			}
			else
			{
				list.remove(0);
				list.add(f);
			}
		
		}
		while(q-->0)
		{
			long qr=in.nextLong();
			if(qr<=(long)y)
			{
				System.out.println(ans[(int) (qr-1)]);
			}
			else
			{
				qr-=y;
				qr%=(n-1);
				if(qr==0)
					qr=n-1;
				System.out.println(max+" "+list.get((int) qr));
				
			}
		}
		
		}
	
	
}
