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.BufferedWriter;
	import java.io.IOException;
	import java.io.InputStream;
	import java.io.OutputStream;
	import java.io.OutputStreamWriter;
	import java.io.PrintWriter;
	import java.io.Writer;
	import java.util.Arrays;
	import java.util.InputMismatchException;
	import java.util.*;
	import java.io.*;
	import java.math.*;
	public class Main7{

	static class Pair
		{ 
			String x="";
			int y; 
			char z;
			public Pair(String x,int y, char z) 
			{	 
				this.z=z;
				this.x = x; 
				this.y = y;
			}	 
		} 
		static class Pair1
		{
			String x;
			int y;
			int z;
			
		}
		static class Compare
		{ 
			static void compare(Pair arr[], int n) 
			{ 
				// Comparator to sort the pair according to second element 
				Arrays.sort(arr, new Comparator<Pair>() { 
					@Override public int compare(Pair p1, Pair p2) 
					{ 
						if(p1.y>p2.y)
						{
							return 1;
						}
						else if(p1.y<p2.y)
						{
							return -1;
						}
						else
						{
							if(p1.z>p2.z)
							{
								return 1;
							}
							else
								return -1;
						}
					} 
				}); 
			}
			static void compare1(Pair arr[], int n) 
			{ 
				// Comparator to sort the pair according to second element 
				Arrays.sort(arr, new Comparator<Pair>() { 
					@Override public int compare(Pair p1, Pair p2) 
					{ 
						if(p1.y>p2.y)
						{
							return 1;
						}
						else if(p1.y<p2.y)
						{
							return -1;
						}
						else
						{
							if(p1.z>p2.z)
							{
								return 1;
							}
							else
								return -1;
						}
					} 
				}); 
			} 
		}
		
	/*	static class pqcomparator implements Comparator<Pair>
		{
		                // for Ascending order of cgpa 
            public int compare(Pair s1, Pair s2) { 
                if (s1.x > s2.x) 
                    return -1; 
                else if (s1.x < s2.x) 
                    return 1; 
                return 0; 
                } 
        } 
		*/
		
		public static long pow(long a, long b)
		{
			long result=1;
			while(b>0)
			{
				if (b % 2 != 0)
				{
					result=(result*a)%mod;
					b--;
				} 
				a=(a*a)%mod;
				b /= 2;
			}   
			return result;
		}
		public static long fact(long num)
		{
					long value=1;
					int i=0;
					for(i=2;i<num;i++)
					{
						value=((value%mod)*i%mod)%mod;
					}
					return value;
				}
				public static int gcd(int a, int b)
				{
					if (a == 0)
						return b;
					return gcd(b%a, a);
				}
				
		/*		public static long lcm(long a,long b)
				{
					return a * (b / gcd(a, b));
				}
			*/	public static long sum(int h)
				{
					return (h*(h+1)/2);
				}
				/*public static void dfs(int parent,boolean[] visited)
				{
					TreeSet<Integer> arr=new TreeSet<Integer>();
					arr=graph.get(parent);
					visited[parent]=true;
					if(a[parent]==1)
					{
						flag=1;
					}
					if(a[parent]==2)
					{
						flag1=1;
					}
					if(flag==1 && flag1==1)
					{
						return;
					}
					Iterator itr=arr.iterator();
					while(itr.hasNext())
					{
						int num=(int)itr.next();
						if(visited[num]==false)
						{
							dfs(num,visited);
						}
					}
					x1x`
				}*/
			//	static int flag1=0;
				static int[] dis;
				static int mod=1000000007;
				static ArrayList<ArrayList<Integer>> graph;
				
				public static void bfs(int num,int size)
				{
					boolean[] visited=new boolean[size+1];
					Queue<Integer> q=new LinkedList<>();
					q.add(num);
					ans[num]=1;
					visited[num]=true;
					while(!q.isEmpty())
					{
						int x=q.poll();
						ArrayList<Integer> al=graph.get(x);
						for(int i=0;i<al.size();i++)
						{
							int y=al.get(i);	
							if(visited[y]==false)
							{
								q.add(y);
								ans[y]=ans[x]+1;
								visited[y]=true;
							}
						}
					}
				}
				static int[] ans;
				
				
				
				
				
				
				
				
				
			//	static int[] a;			  
				
				public static long[] sort(long[] a)
				{
					int n=a.length;
					ArrayList<Long> ar=new ArrayList<>();
					for(int i=0;i<a.length;i++)
					{
						ar.add(a[i]);
					}
					Collections.sort(ar);
					for(int i=0;i<n;i++)
					{
						a[i]=ar.get(i);
					}
					return a;
				}
			//	static int flag=1;
		
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
			
				public static void main(String args[])throws IOException
				{
				//	InputReader in=new InputReader(System.in);
				//	OutputWriter out=new OutputWriter(System.out);
				//	long a=pow(26,1000000005);
				    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			//		ArrayList<Integer> ar4=new ArrayList<>();
				//	ArrayList<Integer> ar2=new ArrayList<>();
					
				//	ArrayList<Integer> ar1=new ArrayList<>();
			//		TreeSet<Integer> ts=new TreeSet<>();
			//		TreeSet<Long> ts1=new TreeSet<>();
				//	HashMap<Long,Integer> hash=new HashMap<>();
					HashMap<Integer,Integer> odd=new HashMap<Integer,Integer>();
					HashMap<Long,Integer> hash2=new HashMap<Long,Integer>();
				/*	boolean[] prime=new boolean[10000001];
					for(int i=2;i*i<=10000000;i++)
					{
						if(prime[i]==false)
						{
							for(int j=2*i;j<=10000000;j+=i)
							{
								prime[j]=true;
							}
						}
					}*/
					int n=i();
					int q1=i();
					int[] a=new int[n];
					int max=0;
					for(int i=0;i<n;i++)
					{
						a[i]=i();
						max=Math.max(max,a[i]);
					}
					Deque<Integer> q=new LinkedList<>();
					for(int i=0;i<n;i++)
					{
						q.add(a[i]);
					}
					int round=0;
					if(q.peekFirst()==max)
					{
						round=0;
					}
					int[][] ans=new int[n][2];
					int count=0;
					while(q.peekFirst()!=max)
					{
						int num=(int)q.pollFirst();
						int num1=(int)q.pollFirst();
						ans[count][0]=num;
						ans[count][1]=num1;
						if(num>num1)
						{
							q.addFirst((Integer)num);
							q.addLast((Integer)num1);
						}
						else
						{
							q.addFirst((Integer)num1);
							q.addLast((Integer)num);
						}
						count++;
					}
					int[] b=new int[n];
					for(int i=0;i<n;i++)
					{
						b[i]=q.pollFirst();
					}
					while(q1-->0)
					{
						long num=l();
						if(num<=count)
						{
							pln(ans[(int)num-1][0]+" "+ans[(int)num-1][1]);
						}
						else
						{
							num=num-(count+1);
							num=num%(n-1);
						//	if(num+1==n)
						//		num=0;
							pln(max+" "+b[(int)num+1]);
						}
					}
				}
				
				
				
				
				
				
				
				
				
				
				
				
				
				
				
				/**/
				static InputReader in=new InputReader(System.in);
					static OutputWriter out=new OutputWriter(System.out);
					public static long l()
					{
						String s=in.String();
						return Long.parseLong(s);
					}
					public static void pln(String value)
					{
						System.out.println(value);
					}
					public static int i()
					{
						return in.Int();
					}
					public static String s()
					{
						return in.String();
					}
		}
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			 
			class InputReader {
				 
				private InputStream stream;
				private byte[] buf = new byte[1024];
				private int curChar;
				private int numChars;
				private SpaceCharFilter filter;
			 
				public InputReader(InputStream stream) {
					this.stream = stream;
				}
			 
				public int read() {
					if (numChars== -1)
						throw new InputMismatchException();
					if (curChar >= numChars) {
						curChar = 0;
						try {
							numChars = stream.read(buf);
						} catch (IOException e) {
							throw new InputMismatchException();
						}
						if (numChars <= 0)
							return -1;
					}
					return buf[curChar++];
				}
			 
				public int Int() {
					int c = read();
					while (isSpaceChar(c))
						c = read();
					int sgn = 1;
					if (c == '-') {
						sgn = -1;
						c = read();
					}
					int res = 0;
					do {
						if (c < '0' || c > '9')
							throw new InputMismatchException();
						res *= 10;
						res += c - '0';
						c = read();
					} while (!isSpaceChar(c));
					return res * sgn;
				}
			 
				public String String() {
					int c = read();
					while (isSpaceChar(c))
						c = read();
					StringBuilder res = new StringBuilder();
					do {
						res.appendCodePoint(c);
						c = read();
					} while (!isSpaceChar(c));
					return res.toString();
				}
			 
				public boolean isSpaceChar(int c) {
					if (filter != null)
						return filter.isSpaceChar(c);
					return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
				}
			 
				public String next() {
					return String();
				}
			 
				public interface SpaceCharFilter {
					public boolean isSpaceChar(int ch);
				}
			}
			 
			class OutputWriter {
				private final PrintWriter writer;
			 
				public OutputWriter(OutputStream outputStream) {
					writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
				}
			 
				public OutputWriter(Writer writer) {
					this.writer = new PrintWriter(writer);
				}
			 
				public void print(Object...objects) {
					for (int i = 0; i < objects.length; i++) {
						if (i != 0)
							writer.print(' ');
						writer.print(objects[i]);
					}
				}
			 
				public void printLine(Object...objects) {
					print(objects);
					writer.println();
				}
			 
				public void close() {
					writer.close();
				}
			 
				public void flush() {
					writer.flush();
				}
			 
				}
			 
				class IOUtils {
			 
				public static int[] readIntArray(InputReader in, int size) {
					int[] array = new int[size];
					for (int i = 0; i < size; i++)
						array[i] = in.Int();
					return array;
				}
			 
				} 