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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.HashMap;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.Map;
import java.io.BufferedReader;
import java.util.ArrayDeque;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Liavontsi Brechka
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CValeraIDek solver = new CValeraIDek();
        solver.solve(1, in, out);
        out.close();
    }

    static class CValeraIDek {
        InputReader in;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            this.in = in;

            int n = ni();
            int q = ni();

            ArrayDeque<Integer> deque = new ArrayDeque<>();
            int max = 0;
            for (int i = 0; i < n; i++) {
                int next = ni();
                max = Math.max(max, next);
                deque.offer(next);
            }

            Map<Integer, CValeraIDek.Pair> pre = new HashMap<>();
            int mInit = 0;

            assert deque.size() >= 2;
            while (deque.peek() != max) {
                mInit++;

                CValeraIDek.Pair next = new CValeraIDek.Pair(deque.poll(), deque.poll());
                pre.put(mInit, next);

                if (next.a > next.b) {
                    deque.push(next.a);
                    deque.offer(next.b);
                } else {
                    deque.push(next.b);
                    deque.offer(next.a);
                }
            }

            int[] finalArr = new int[n];
            for (int i = 0; i < n; i++) {
                finalArr[i] = deque.poll();
            }

            StringBuilder res = new StringBuilder();
            for (int i = 0; i < q; i++) {
                long m = nl();

                if (m <= mInit) {
                    CValeraIDek.Pair next = pre.get((int) m);
                    res.append(next.a).append(' ').append(next.b).append('\n');
                } else {
                    m -= mInit;
                    m %= (n - 1);
                    if (m == 0) m = n - 1;
                    res.append(max).append(' ').append(finalArr[(int) m]).append('\n');
                }
            }

            out.println(res);
        }

        private int ni() {
            return in.nextInt();
        }

        private long nl() {
            return in.nextLong();
        }

        static class Pair {
            int a;
            int b;

            public Pair(int a, int b) {
                this.a = a;
                this.b = b;
            }

        }

    }

    static class InputReader {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

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

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(readLine());
            }
            return tokenizer.nextToken();
        }

        public String readLine() {
            String line;
            try {
                line = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }

    }
}

