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. 

/*
9 2
        1 1 1 1 1 0 0 0 0
        1 2
        1 5
        5 6
        5 7
        2 3
        2 4
        3 8
        3 9
*/


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

public class Question {


    static LinkedList<Integer> adj[];
    static boolean[] visited;
    static boolean[] visited_;
    static int[] ans;
    static int count_ = 0;
    static final int MAX_SIZE = 1000001;
    static Vector<Boolean> isprime = new Vector<>(MAX_SIZE);
    static Vector<Integer> prime = new Vector<>();
    static Vector<Integer> SPF = new Vector<>(MAX_SIZE);

    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        long n = Reader.nextLong();
        long q = Reader.nextLong();
        LinkedList<Long> list = new LinkedList<>();
        for (int i = 0 ; i < n ; i++){
            list.addLast(Reader.nextLong());
        }
        long[][] ans = new long[(int)n][2];
        for (int i = 0 ; i < n ; i++){
            long num1 = list.removeFirst();
            long num2 = list.removeFirst();
            ans[i][0] = num1;
            ans[i][1] = num2;
            list.addLast(Math.min(num1,num2));
            list.addFirst(Math.max(num1,num2));
        }
        long[] xarr = new long[(int)n];
        for (int i = 0 ; i < n ; i++){
            xarr[i] = list.removeFirst();
        }
        /*for (int i = 0 ; i < xarr.length ; i++){
            System.out.print(xarr[i] + " ");
        }
        System.out.println();*/
        while (q-->0){
            long query = Reader.nextLong();
            if (query>n) {
                query-=n;
                long mod = query % (n - 1);
                if (mod==0){
                    mod = n-1;
                }
                //System.out.println("mod " +mod );
                System.out.println(xarr[0] + " " + xarr[(int) mod]);
            }
            else{
                System.out.println(ans[(int)query-1][0] + " " + ans[(int)query-1][1]);
            }
        }






    }
    public static void sortbyColumn(int arr[][], int col)
    {
        // Using built-in sort function Arrays.sort
        Arrays.sort(arr, new Comparator<int[]>() {

            @Override
            // Compare values according to columns
            public int compare(final int[] entry1,
                               final int[] entry2) {

                // To sort in descending order revert
                // the '>' Operator
                if (entry1[col] > entry2[col])
                    return 1;
                else
                    return -1;
            }
        });  // End of function call sort().
    }
}

class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }

    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}
class MergeSort {
    // Merges two subarrays of arr[].
    // First subarray is arr[l..m]
    // Second subarray is arr[m+1..r]
    void merge(int arr[], int l, int m, int r) {
        // Find sizes of two subarrays to be merged
        int n1 = m - l + 1;
        int n2 = r - m;

        /* Create temp arrays */
        int L[] = new int[n1];
        int R[] = new int[n2];

        /*Copy data to temp arrays*/
        for (int i = 0; i < n1; ++i)
            L[i] = arr[l + i];
        for (int j = 0; j < n2; ++j)
            R[j] = arr[m + 1 + j];


        /* Merge the temp arrays */

        // Initial indexes of first and second subarrays
        int i = 0, j = 0;

        // Initial index of merged subarry array
        int k = l;
        while (i < n1 && j < n2) {
            if (L[i] <= R[j]) {
                arr[k] = L[i];
                i++;
            } else {
                arr[k] = R[j];
                j++;
            }
            k++;
        }

        /* Copy remaining elements of L[] if any */
        while (i < n1) {
            arr[k] = L[i];
            i++;
            k++;
        }

        /* Copy remaining elements of R[] if any */
        while (j < n2) {
            arr[k] = R[j];
            j++;
            k++;
        }
    }

    // Main function that sorts arr[l..r] using
    // merge()
    void sort(int arr[], int l, int r) {
        if (l < r) {
            // Find the middle point
            int m = (l + r) / 2;

            // Sort first and second halves
            sort(arr, l, m);
            sort(arr, m + 1, r);

            // Merge the sorted halves
            merge(arr, l, m, r);
        }
    }

    /* A utility function to print array of size n */
    static void printArray(int arr[]) {
        int n = arr.length;
        for (int i = 0; i < n; ++i)
            System.out.print(arr[i] + " ");
        System.out.println();
    }

    static long phi(long n,long R)
    {

        long result = R;


        for (long p = 2; p * p <= n; ++p)
        {


            if (n % p == 0)
            {


                while (n % p == 0)
                    n =n/p;
                result =result - ( result / p);
            }
        }


        //System.out.println("n" + n);
        if (n > 1)
            result -= result / n;
        return result;
    }
}

class person{
    int index;
    int money;

    public person(int index, int money) {
        this.index = index;
        this.money = money;
    }

    public void setIndex(int index) {
        this.index = index;
    }

    public void setMoney(int money) {
        this.money = money;
    }

    public int getIndex() {
        return index;
    }

    public int getMoney() {
        return money;
    }
}

class StudentComparator implements Comparator<person>{

    // Overriding compare()method of Comparator
    // for descending order of cgpa
    public int compare(person s1, person s2) {
        if (s1.money > s2.money)
            return 1;
        else if (s1.money < s2.money) {
            return -1;
        }
        else{
            if (s1.index >s2.index){
                return 1;
            }
            else{
                return -1;
            }
        }

    }
}


