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.util.*;
	import java.io.*;
	
			public class codeforces
			{	
				public static long M = 1000000007;
				
				public static void main(String[] args)
				{
					InputReader in = new InputReader(System.in);
					PrintWriter pw = new PrintWriter(System.out);
					
					int n = in.nextInt();
					int q = in.nextInt();
					long[] a = new long[n];
					Deque<Long> dq = new LinkedList<>();
					HashMap<Integer, Long> map1 = new HashMap<>();
					HashMap<Integer, Long> map2 = new HashMap<>();
					
					for(int i=0;i<n;i++)
					{
						a[i] = in.nextInt();
						dq.addLast(a[i]);
					}
					//pw.println(dq);
					for(int i=0;i<n-1;i++)
					{
						long A = dq.removeFirst();
						long B = dq.removeFirst();
						//pw.println(dq);
						//pw.println(A);
						map1.put(i+1, A);
						map2.put(i+1, B);
						dq.addLast(Math.min(A, B));
						dq.addFirst(Math.max(A, B));
					}
					//pw.println(dq);
					long max = 0;
					int index = 0;
					for(long k : dq)
					{
						if(index == 0)
							max = k;
						
						a[index] = k;
						index++;
					}
					//pw.println(Arrays.toString(a));
					while(q-- > 0)
					{
						long x = in.nextLong();
						int mod = 0;
						
						if(x >= n)
						{
							mod = (int)(x%(long)(n-1));
							if(mod == 0)
								mod = n-1;
							pw.println(max+" "+a[mod]);
						}
						else
						{
							pw.println(map1.get((int)x)+" "+map2.get((int)x));
						}
						
					}
					pw.flush();
					pw.close();
				}
				
				public static long[][] matrixpower(long[][] mat, long n)
				{
					int r = mat.length;
					long[][] ans = new long[r][r];
					
					for(int i=0;i<r;i++)
						ans[i][i] = 1;
					
					while(n > 0)
					{
						if(n%2 == 1)
							ans = matrixmultiply(ans, mat);
						mat = matrixmultiply(mat, mat);
						n /= 2;
					}
					
					return ans;
				}
				
				public static long[][] matrixmultiply(long[][] M1, long[][] M2)
				{
					int m1 = M1.length, m2 = M2[0].length;
					long[][] ans = new long[m1][m2];
					
					for(int i=0;i<m1;i++)
					{
						for(int j=0;j<m2;j++)
						{
							for(int k=0;k<M2.length;k++)
								ans[i][j] = (ans[i][j]%(M-1) + ((M1[i][k]%(M-1))*(M2[k][j]%(M-1)))%(M-1))%(M-1);
						}
						//System.out.println(Arrays.toString(ans[i]));
					}
					return ans;
				}
				
				public static long prime(long nth) {
				    
				    long num, count, i;
				    num=1;
				    count=0;
				 
				    while (count < nth){
				      num=num+1;
				      for (i = 2; i <= num; i++){ //Here we will loop from 2 to num
				        if (num % i == 0) {
				          break;
				        }
				      }
				      if ( i == num){//if it is a prime number
				        count = count+1;
				      }
				    }
				    return num;
				  }
			  
				
				public static int[] suffle(int[] a,Random gen)
				{
					int n = a.length;
					for(int i=0;i<n;i++)
					{
						int ind = gen.nextInt(n-i)+i;
						int temp = a[ind];
						a[ind] = a[i];
						a[i] = temp;
					}
					return a;
				}
				
				public static long modularExponentiation(long x,long n,long M)
				{
				    long result=1;
				    while(n>0)
				    {
				        if(n % 2 ==1)
				            result=(result * x)%M;
				        x=(x*x)%M;
				        n=n/2;
				    }
				    return result;
				}
				
				public static long modInverse(long A,long M)
				{
				    return modularExponentiation(A,M-2,M);
				}
				
				public static int BinarySearch_l(long[] a, long k)
				{
					int n = a.length;
					int i = 0, j = n-1;
					int mid = 0;
					
					if(k - a[n-1] > 0)
						return n;
					else
					{
						while(j - i > 0)
						{
							mid = (i+j)/2;
							
							if(k - a[mid] > 0)
								i = mid + 1;
							else
								j = mid;
						}
					}
					
					return i;
				}
				
				public static int BinarySearch_r(long[] a, long k)
				{
					int n = a.length;
					int i = 0, j = n-1;
					int mid = 0;
					
					if(k - a[0] < 0)
						return -1;
					else
					{
						while(j - i > 0)
						{
							mid = (int)Math.ceil((double)(i+j)/2);
							
							if(k - a[mid] >= 0)
								i = mid;
							else
								j = mid - 1;
						}
					}
					
					return i;
				}
				public static long fact(long n, long M)
				{
					long ans = 1;
					
					for(long i=n;i>0;i--)
					{
						ans = (ans*i)%M;
					}
					
					return ans;
				}
				
			/*	public static void DFS(int sourse)
				{
					int count = 0;
					visited[sourse] = true;
					
					for(int u : adj[sourse])
					{
						if(!visited[u])
						{
							DFS(u);
						}
					}
					
					
				}*/
				
				public static ArrayList Divisors(int n)
				{
				    ArrayList<Integer> div = new ArrayList<>();
				    
				    for (int i=1; i<=Math.sqrt(n); i++)
				    {
				        if (n%i == 0)
				        {
				        	div.add(i);
				                
				            if(n/i != i)
				            	div.add(n/i);
				        }
				    }
				    return div;
				}
			
				public static long GCD(long a,long b)
				{
					if(b==0)
						return a;
					else
						return GCD(b,a%b);
				}
				
				public static long LCM(long a,long b)
				{
					return (a*b)/GCD(a, b);
				}
				
				static class pair implements Comparable<pair>
				{
					Integer x, y;
					pair(int x,int y)
					{
						this.x=x;
						this.y=y;
					}
					
					public int compareTo(pair o) {
						int result = x.compareTo(o.x);
						if(result==0)
							result = y.compareTo(o.y);
						
						return result;
					}  
					
					public String toString()
					{
						return x+" "+y;
					}
					
					public boolean equals(Object o)
					{
						if (o instanceof pair)
					    {
							pair p = (pair)o;
							return p.x - x == 0 && p.y - y == 0 ;
						}
						return false;
					}
					
					public int hashCode()
					{
						return new Long(x).hashCode()*31 + new Long(y).hashCode();
					}
				}
				
				static class InputReader 
				{
					 
					private final InputStream stream;
					private final byte[] buf = new byte[8192];
					private int curChar, snumChars;
					private SpaceCharFilter filter;
			 
					public InputReader(InputStream stream) 
					{
						this.stream = stream;
					}
			 
					public int snext() 
					{
						if (snumChars == -1)
							throw new InputMismatchException();
						if (curChar >= snumChars) 
						{
							curChar = 0;
							try 
							{
								snumChars = stream.read(buf);
							} 
							catch (IOException e) 
							{
								throw new InputMismatchException();
							}
							if (snumChars <= 0)
								return -1;
						}
						return buf[curChar++];
					}
			 
					public int nextInt() 
				    {
						int c = snext();
						while (isSpaceChar(c)) 
						{
							c = snext();
						}
						int sgn = 1;
						if (c == '-')
					    {
							sgn = -1;
							c = snext();
						}
						int res = 0;
						do 
						{
							if (c < '0' || c > '9')
								throw new InputMismatchException();
							res *= 10;
							res += c - '0';
							c = snext();
						} while (!isSpaceChar(c));
						return res * sgn;
					}
			 
					public long nextLong()
				    {
						int c = snext();
						while (isSpaceChar(c)) 
						{
							c = snext();
						}
						int sgn = 1;
						if (c == '-') 
						{
							sgn = -1;
							c = snext();
						}
						long res = 0;
						do 
						{
							if (c < '0' || c > '9')
								throw new InputMismatchException();
							res *= 10;
							res += c - '0';
							c = snext();
						} while (!isSpaceChar(c));
						return res * sgn;
					}
			 
					public int[] nextIntArray(int n) 
					{
						int a[] = new int[n];
						for (int i = 0; i < n; i++) 
						{
							a[i] = nextInt();
						}
						return a;
					}
			 
					public String readString()
				    {
						int c = snext();
						while (isSpaceChar(c)) 
						{
							c = snext();
						}
						StringBuilder res = new StringBuilder();
						do 
						{
							res.appendCodePoint(c);
							c = snext();
						} while (!isSpaceChar(c));
						return res.toString();
					}
			 
					public String nextLine() 
					{
						int c = snext();
						while (isSpaceChar(c))
							c = snext();
						StringBuilder res = new StringBuilder();
						do 
						{
							res.appendCodePoint(c);
							c = snext();
						} while (!isEndOfLine(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;
					}
			 
					private boolean isEndOfLine(int c) 
					{
						return c == '\n' || c == '\r' || c == -1;
					}
			 
					public interface SpaceCharFilter
				    {
						public boolean isSpaceChar(int ch);
					}
				}
				
				static class CodeX {
		        public static void sort(long arr[]) {
		            merge_sort(arr, 0, arr.length - 1);
		        }
		
		        private static void merge_sort(long A[], long start, long end) {
		            if (start < end) {
		                long mid = (start + end) / 2;
		                merge_sort(A, start, mid);
		                merge_sort(A, mid + 1, end);
		                merge(A, start, mid, end);
		            }
		
		        }
		
		        private static void merge(long A[], long start,long mid, long end) {
		            long p = start, q = mid + 1;
		            long Arr[] = new long[(int)(end - start + 1)];
		            long k = 0;
		
		            for (int i = (int)start; i <= end; i++) {
		                if (p > mid)
		                    Arr[(int)k++] = A[(int)q++];
		
		                else if (q > end)
		                    Arr[(int)k++] = A[(int)p++];
		
		                else if (A[(int)p] < A[(int)q])
		                    Arr[(int)k++] = A[(int)p++];
		
		                else
		                    Arr[(int)k++] = A[(int)q++];
		            }
		            for (int i = 0; i < k; i++) {
		                A[(int)start++] = Arr[i];
		            }
		
		        }
		
		    }
			}	
			
	
				