Problem:
Score : 300 points

Problem Statement

Given are an integer X and an integer sequence of length N: p_1, \ldots, p_N.

Among the integers not contained in the sequence p_1, \ldots, p_N (not necessarily positive), find the integer nearest to X, that is, find the integer whose absolute difference with X is the minimum. If there are multiple such integers, report the smallest such integer.

Constraints

1 \leq X \leq 100

0 \leq N \leq 100

1 \leq p_i \leq 100

p_1, \ldots, p_N are all distinct.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X N
p_1 ... p_N

Output

Print the answer.

Sample Input 1

6 5
4 7 10 6 5

Sample Output 1

8

Among the integers not contained in the sequence 4, 7, 10, 6, 5, the one nearest to 6 is 8.

Sample Input 2

10 5
4 7 10 6 5

Sample Output 2

9

Among the integers not contained in the sequence 4, 7, 10, 6, 5, the ones nearest to 10 are 9 and 11. We should print the smaller one, 9.

Sample Input 3

100 0

Sample Output 3

100

When N = 0, the second line in the input will be empty. Also, as seen here, X itself can be the answer.

Solution in Fortran (GNU Fortran 9.2.1) (judge verdict: Wrong Answer)

   program abc170c
      implicit none
      integer::x,n
      integer,allocatable,dimension(:)::p
      logical,allocatable,dimension(:)::check
      integer::i,step


         read *, x,n
         allocate( p(n),check(-100:200) )
         check=.false.
         read *, p(1:n)

         if ( n==0 ) then
            print *, x
            stop
         end if

         do i=1,n
            check(p(i))=.true.
         end do

         if ( check(x) .eqv. .false. ) then
            print *, x
            stop
         end if

         step=0
         do while ( check(x+step) .and. check(x-step) )
            step=step+1
            if ( check(x+step) .eqv. .false. ) then
               if ( check(x-step) .eqv. .false. ) then
                  print *, x-step
                  stop
               else
                  print *, x+step
                  stop
               end if
            end if
         end do


   end program abc170c