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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class deque_prob {

    private static ArrayList<Integer> getIntInput(BufferedReader br){
        ArrayList<Integer> input = new ArrayList<>();
        try {
            String[] inputStr = br.readLine().trim().split(" ");
            for(String s: inputStr){
                input.add(Integer.parseInt(s));
            }
        } catch (IOException e) {
            e.printStackTrace();
        }
        return input;
    }

    private static ArrayList<Long> getLongInput(BufferedReader br){
        ArrayList<Long> input = new ArrayList<>();
        try {
            String[] inputStr = br.readLine().trim().split(" ");
            for(String s: inputStr){
                input.add(Long.parseLong(s));
            }
        } catch (IOException e) {
            e.printStackTrace();
        }
        return input;
    }


    public static void main(String[] args) {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        List<Integer> list = getIntInput(br);
        int n = list.get(0);
        int q = list.get(1);

        list = getIntInput(br);

        if(q==0){
            return;
        }

        Deque<Integer> dq = new ArrayDeque<>(list);

        Iterator<Integer> it = dq.iterator();
        int max = Integer.MIN_VALUE;
        while(it.hasNext()){
            int temp = it.next();
            max = Math.max(temp, max);
        }

        ArrayList<ArrayList<Integer>> arr = new ArrayList<>();

        while(true){
            int first = dq.pop();
            int second = dq.pop();
            arr.add(new ArrayList<Integer>());
            arr.get(arr.size()-1).add(first);
            arr.get(arr.size()-1).add(second);
            if(first > second){
                dq.addFirst(first);
                dq.addLast(second);
            } else {
                dq.addFirst(second);
                dq.addLast(first);
            }
            if(max == first || max == second){
                break;
            }
        }

        dq.pop();
        ArrayList<Integer> rest = new ArrayList<>();
        while(dq.size() > 0){
            rest.add(dq.pop());
        }

        while(q>0){
            long ii = getLongInput(br).get(0);

            if(ii <= arr.size()){
                System.out.print(arr.get((int)ii-1).get(0) + " "+ arr.get((int)ii-1).get(1) +"\n");
            } else {
                long temp = ii-arr.size();
                long ind = (temp-1) % (n-1);
                System.out.print(max + " "+ rest.get((int)ind)+"\n");
            }
            q--;
        }
    }
}
