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>
using namespace std;
#define PI 3.14159265358979323
#define ll long long int
#define vi vector <int>
#define vl vector <ll>
#define all(v) (v).begin(),(v).end()
#define pb push_back
 
ll power(ll a, ll b){//a^b
    ll res=1;
    while(b>0){
        if(b&1){res=(res*a);b--;}
        a=(a*a);
        b>>=1;
    }
    return res;
}

ll gcd(ll a, ll b){return (b==0)?a:gcd(b,a%b);}

int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	ll x,n;
	cin>>x>>n;
	set <ll> s;
	for(ll i=1;i<=100;i++)
		s.insert(i);
	for(ll i=0;i<n;i++){
		ll temp;
		cin>>temp;
		s.erase(temp);
	}

	set <ll> :: iterator a=upper_bound(all(s),x);
	if(s.size()==0){
		cout<<0<<"\n";
		return 0;
	}
	if(a==s.begin())
		cout<<((*a)-x>x?0:*a)<<"\n";
	else if(a==s.end())
		cout<<*(--a)<<"\n";
	else{
		set <ll> :: iterator b=a;
		b--;
		if((x-(*b))<=((*a)-x))
			cout<<*b<<"\n";
		else
			cout<<*a<<"\n";
	}
}