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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <string>
#include <vector>

using namespace std;

int main() {
  int num;
  int sequence_num;
  vector<int> sequence;

  cin >> num >> sequence_num;
  sequence.resize(sequence_num);
  for(int i = 0; i < sequence_num; i++) {
    cin >> sequence[i];
  }

  if(sequence_num == 0) {
    cout << num << endl;
    return 0;
  }

  int target_num;
  for(int distance = 1; distance <= sequence_num / 2.0; distance++) {
    int less_target = num - distance;
    int grater_tagert = num + distance;

    bool not_included_less = true;
    bool not_included_greater = true;
    for(int i = 0; i < sequence_num; i++) {
      if(sequence[i] == less_target) {
        not_included_less = false;
      }
      if(sequence[i] == grater_tagert) {
        not_included_greater = false;
      }
    }

    if(not_included_less) {
      target_num = less_target;
      break;
    }
    if(not_included_greater) {
      target_num = grater_tagert;
      break;
    }
  }

  cout << target_num << endl;
}