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: Accepted)

program main
    use,intrinsic :: iso_fortran_env
    implicit none
    integer(int32):: cnt(0:101), x,n,i,l,r
    integer(int32), allocatable:: p(:)

    read*, x,n
    allocate(p(n))
    read*, p(:)
    cnt(:) = 0
    do i=1,n
        cnt(p(i))=cnt(p(i))+1
    end do

    l=x
    r=x

    do while(0 /= l .or. r /= 101)
        if (cnt(l) == 0) then
            print'(i0)', l 
            stop
        end if

        if (cnt(r) == 0) then
            print'(i0)', r
            stop
        end if

        l=max(l-1,0)
        r=min(r+1,101)
    end do
end program main