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 Ruby (2.7.1) (judge verdict: Wrong Answer)

x, n = gets.to_s.split.map(&:to_i)
p_arr = gets.to_s.split.map(&:to_i)

sort_arr = p_arr.sort_by { |pi| [(x - pi).abs, pi] }

p_arr.length.times do |i|
  diff = (i + 1) / 2
  expected = i % 2 == 1 ? x - diff : x + diff
  if sort_arr[i] != expected
    puts expected
    exit
  end
end

i = p_arr.length - 1
diff = (i + 1) / 2
expected = i % 2 == 1 ? x - diff : x + diff

puts expected