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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.StringTokenizer; 
						  
						
						public class temp4 {
							static class FastReader 
						    { 
						        BufferedReader br; 
						        StringTokenizer st; 
						  
						        public FastReader() 
						        { 
						            br = new BufferedReader(new
						                     InputStreamReader(System.in)); 
						        } 
						  
						        String next() 
						        { 
						            while (st == null || !st.hasMoreElements()) 
						            { 
						                try
						                { 
						                    st = new StringTokenizer(br.readLine()); 
						                } 
						                catch (IOException  e) 
						                { 
						                    e.printStackTrace(); 
						                } 
						            } 
						            return st.nextToken(); 
						        } 
						  
						        int nextInt() 
						        { 
						            return Integer.parseInt(next()); 
						        } 
						  
						        long nextLong() 
						        { 
						            return Long.parseLong(next()); 
						        } 
						  
						        double nextDouble() 
						        { 
						            return Double.parseDouble(next()); 
						        } 
						  
						        String nextLine() 
						        { 
						            String str = ""; 
						            try
						            { 
						                str = br.readLine(); 
						            } 
						            catch (IOException e) 
						            { 
						                e.printStackTrace(); 
						            } 
						            return str; 
						        } 
						    } 
							
						/*	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 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(); 
						        } 
						    } */
							static class Print
						{
							    private final BufferedWriter bw;
							    public Print()
							    {
							        bw=new BufferedWriter(new OutputStreamWriter(System.out));
							    }
						    public void print(String str)throws IOException
							    {
							        bw.append(str);
							    }
							    public void println(String str)throws IOException
							    {
							        print(str);
							        bw.append("\n");
							    }
							    public void close()throws IOException
							    {
							        bw.close();
							    }} 
								
								
								
								public static void main(String[] args) throws IOException {			
									FastReader scn=new FastReader();
									Print pr=new Print();
									int n=scn.nextInt(),q=scn.nextInt();
									int[] arr=new int[n+1],max=new int[n+1],min=new int[n+1];
									
									for(int i=1;i<=n;i++){
										arr[i]=scn.nextInt();
									}
									max[1]=arr[1];
									for(int i=2;i<=n;i++){
										max[i]=Math.max(arr[i],max[i-1]);
										if(max[i]==arr[i]) min[i-1]=max[i-1];
										else min[i-1]=arr[i];
									}
									long x=0;
									for(int i=0;i<q;i++){
										x=scn.nextLong();
										if(x<n){
											pr.println(max[(int) x]+" "+arr[(int) (x+1)]);
										}
										else{
											pr.println(max[n]+" "+min[(int) ((x-1)%(n-1)+1)]);
										}
									}
									
								
									pr.close();
								}
								public static class node{
									int a;
									int b;
									public node(int a,int b){
										this.a=a;this.b=b;
									}
								}
								
						}
							