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.io.*;

public class Solution{

	public static Integer INT(String s) {
		return Integer.parseInt(s);
	}

	public static Long LONG(String s) {
		return Long.parseLong(s);
	}

	public static String STR(int arr[]) {
		return Arrays.toString(arr);
	}

	public static String STR(long arr[]) {
		return Arrays.toString(arr);
	}

	static int mod=1_000_000_007;

	//==================================================================================================================================================



	public static void main(String args[]) throws IOException {

		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));	Scanner in=new Scanner(System.in); StringBuilder out=new StringBuilder();
		
		int n=in.nextInt(),
			q=in.nextInt();

		LinkedList<Integer> list=new LinkedList<>();

		int max=0;
		for(int i=0; i<n; i++) {
			int item=in.nextInt();
			list.add(item);
			max=Math.max(max, item);
		}

		HashMap<Long, String> map=new HashMap<>();
		long k=1;
		while(list.getFirst()!=max) {
			int A=list.poll(),
				B=list.poll();
			map.put(k++, A+" "+B);
			list.add(Math.min(A, B));
			list.addFirst(Math.max(A, B));
		}

		int a[]=new int[n-1];
		list.poll();
		for(int i=0; i<n-1; i++)
			a[i]=list.poll();

		while(q--!=0) {
			long m=in.nextLong();
			if(m<k)
				out.append(map.get(m));
			else {
				m-=k;
				m%=(long)(n-1);

				out.append(max+" "+a[(int)m]);
			}
			out.append("\n");
		}

		System.out.println(out);
	}
}	