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 <cstdio>
#include <iostream>
#include <iomanip>
#include <string>
#include <cmath>
#include <vector>
#include <algorithm>
using namespace std;
 
int main() {
    
    int X,N;
    int answer=0;
    int dis=9999;
    bool match=false;
    cin>>X>>N;
    if(N==0){
      cout<<X<<endl;
      return 0;
    }
    vector<int> p(N);
    for(int i=0;i<N;i++)
    {
       cin>>p[i];
    }
    sort(p.begin(),p.end());
    //p.pop_back();
    //reverse(p.begin(),p.end());
    /*for(int i=0;i<N;i++)
    {
      cout<<p[i]<<endl;
    }*/
    for(int i=0;i<N-1;i++)
    {
      for(int t=p[i]+1;t<p[i+1];t++)
      {
        //cout<<"abs"<<abs(t-X)<<endl;
        if(abs(X-t)<dis){
          answer=t;
          dis=abs(X-t);
          match=true;
          //cout<<t<<endl;
        }
      }
    }
    if(match){
        cout<<answer<<endl;
    }
    else
    {
        cout<<p[0]-1<<endl;
    }
    return 0;
}