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.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.ArrayDeque;

public class C {
	public static class Pair {
		int x;
		int y;
		Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}
	}

	public static void main(String[] args) throws IOException {
		Reader sc = new Reader();
		int n = sc.nextInt(), q = sc.nextInt();
		ArrayDeque<Integer> d = new ArrayDeque<>();
		int max = -1, inx = -1;
		int a;
		for (int i = 0; i < n; i++) {
			a = sc.nextInt();
			d.addLast(a);
			if (a > max) {
				max = a;
				inx = i;
			}
		}

		TreeMap<Long, Pair> map = new TreeMap<>();
		for (long i = 0; i < inx; i++) {
			int first = d.pollFirst();
			int second = d.pollFirst();
			map.put(i + 1, new Pair(first, second));
			if (first < second) {
				int buf = first;
				first = second;
				second = buf;
			}
			d.addFirst(first);
			d.addLast(second);
		}

		int[] res = new int[n];
		for (int i = 0; i < n; i++) {
			int first = d.pollFirst();
			res[i] = first;
		}

		long req;
		for (int i = 0; i < q; i++) {
			req = sc.nextLong();
			if (req <= inx) {
				Pair p = map.get(req);
				System.out.println(p.x + " " + p.y);
			} else {
				System.out.println(res[0] + " " + res[(int)((req - (inx + 1)) % (n - 1) + 1)]);
			}
		}


	}


	public static class Reader {
	final private int BUFFER_SIZE = 1 << 16;
	private DataInputStream din;
	private byte[] buffer;
	private int bufferPointer, bytesRead;
	public Reader() {
		din = new DataInputStream(System.in);
		buffer = new byte[BUFFER_SIZE];
		bufferPointer = bytesRead = 0;
	}

	public Reader(String file_name) throws IOException {
		din = new DataInputStream(new FileInputStream(file_name));
		buffer = new byte[BUFFER_SIZE];
		bufferPointer = bytesRead = 0;
	}

	public String readLine() throws IOException {
		byte[] buf = new byte[64]; // line length
		int cnt = 0, c;
		while((c = read()) != -1) {
			if (c == '\n') break;
			buf[cnt++] = (byte) c;
		}
		return new String(buf, 0, cnt);
	}

	public String next() throws IOException {
		byte[] buf = new byte[64]; // word length
		int cnt = 0;
		byte c = read();
		while (c == ' ' || c == '\n')
			c = read();
		do {
			if (c == '\n' || c == ' ') break;
			buf[cnt++] = (byte) c;
		} while((c = read()) != -1);
		return new String(buf, 0, cnt);
	}

	public int nextInt() throws IOException {
		int ret = 0;
		byte c = read();
		while (c <= ' ')
			c = read();
		boolean neg = (c == '-');
		if (neg)
			c = read();
		do {
			ret = ret * 10 + c - '0';
		} while ((c = read()) >= '0' && c <= '9');

		if (neg) 
			return -ret;
		return ret;
	}

	public long nextLong() throws IOException {
		long ret = 0;
		byte c = read();
		while (c <= ' ')
			c = read();
		boolean neg = (c == '-');
		if (neg)
			c = read();
		do {
			ret = ret * 10 + c - '0';
		} while ((c = read()) >= '0' && c <= '9');

		if (neg) 
			return -ret;
		return ret;
	}

	public double nextDouble() throws IOException {
		double ret = 0, div = 1;
		byte c = read();
		while(c <= ' ') c = read();
		boolean neg = (c == '-');
		if (neg) c = read();

		do {
			ret = ret * 10 + c - '0';
		} while ((c = read()) >= '0' && c <= '9');

		if (c == '.') {
			while ((c = read()) >= '0' && c <= '9') {
				ret += (c - '0') / (div *= 10);
			}
		}

		if (neg) return -ret;
		return ret;
	}

	private void fillBuffer() throws IOException {
		bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
		if (bytesRead == -1) buffer[0] = -1;
	}

	private byte read() throws IOException {
		if (bufferPointer == bytesRead) fillBuffer();
		return buffer[bufferPointer++];
	}

	public void close() throws IOException {
		if (din == null) return;
		din.close();
	}

	public static void main(String[] args) throws IOException {
		Reader reader = new Reader();
		System.out.println(reader.next());
		System.out.println(reader.next());
		System.out.println(reader.next());
	}
}
}