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.ArrayList;
import java.util.Deque;
import java.util.LinkedList;
import java.util.Scanner;

public class Main {

    static class Pair {
        int a;
        int b;
        public Pair(int a, int b){
            this.a = a;
            this.b = b;
        }
    }
    public static void main(String[] args) {

        ArrayList<Pair> pairs = new ArrayList<>();
        ArrayList<Integer> list = new ArrayList<>();
        ArrayList<Long> query = new ArrayList<>();
        Deque<Integer> deque = new LinkedList<>();
        Scanner sc  = new Scanner(System.in);
        int n = sc.nextInt();
        int q = sc.nextInt();
        int max = Integer.MIN_VALUE;
        for(int i=0;i<n;i++) {
            int add = sc.nextInt();
            deque.addLast(add);
            if(add > max) {
                max = add;
            }
        }
        for(int i=0; i<q; i++) {
            query.add(sc.nextLong());
        }
        while(deque.peekFirst() != max) {
            int a = deque.pollFirst();
            int b = deque.pollFirst();
            pairs.add(new Pair(a,b));
            if(a > b) {
                deque.addFirst(a);
                deque.addLast(b);
            }
            else {
                deque.addFirst(b);
                deque.addLast(a);
            }
        }
        deque.removeFirst();
        while(!deque.isEmpty()) {
            list.add(deque.removeFirst());
        }
        long counter = pairs.size();
        for(int i=0; i<q; i++) {
            if(query.get(i) <= counter) {
                long index = query.get(i);
                System.out.println(pairs.get((int)index-1).a + " " + pairs.get((int)index-1).b );
            }
            else {
                long index = query.get(i) - counter;
                index = index%list.size();
                if(index == 0) index = list.size();
                System.out.println(max + " " + list.get((int)index-1));

            }
        }

    }
}
