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 <bits/stdc++.h>
#include <iostream>
typedef long long ll;
#define rep(i,a,b) for(ll i =a ;i <= b;i++)
#define per(i,a,b) for(ll i =a ;i >= b;i--)
using namespace std;


int main(int argc, char const *argv[])
{
	//ifstream cin("input.txt");
	
	int x, n,p;
	cin>>x>>n;
	if(n == 0){
			cout<<x;
			return 0;
	}
	set<int> s;
	rep(i,0, n-1){
		cin>>p;
		s.insert(p);
	}
	
	auto a = s.upper_bound( x);
	auto b = s.lower_bound(x - 1);

	if(*b == x)
		cout<<x-1;
	else if(*a > x+1)
		cout<<x+1;
	else
	{
		if(x + 1 == *a && x-1 ==*b)
		{
			int i = *b-1, j = *a+1;
			auto r = s.find(i);
			auto l = s.find(j);
			while(r != s.end() && l != s.end())
			{
				i--;j++;
				r = s.find(j);
				l = s.find(i);
			}
			if(l == s.end())
				cout<<i;
			else
				cout<<j;
		}
		else if(x+1 != *a)
			cout<<x+1;
		else
			cout<<x-1;
	}
		
}