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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;
import java.io.* ;
/*
NOTES:
-more than 10 digits (10^10), use long
-prefix sum of 1's and -1's to control flow of highlighting a region
-log(a)/log(b) = log base b of a
-create a position array if trying to see if elements show up next to each other sequentially
 i.e. elements 1,2,3 are within 3 spots of each other in an array
      arr[scannedInt - 1] = i; (position of i at p[i] in original)
- use a freq array when counting instances of an element occurring
- increment the counter first before simulating anything turn-based (two player game)

 */

public class Main {
    static long mod = (long)(Math.pow(10, 9) + 7);
    public static String alpha = "zabcdefghijklmnopqrstuvwxy";
    public static void main(String[] args) throws IOException{
        Scanner scan = new Scanner(System.in);
        long t = 1;
        while (t-- > 0) {
            int[] diff = new int[1000];
            int x= scan.nextInt();
            int n = scan.nextInt();
            ArrayList<Integer> arr = new ArrayList<>();
            for(int i = 0; i<n; i++){
                arr.add(scan.nextInt());
                diff[Math.abs(x-arr.get(i))]++;
            }
            int small = 0, big = 0;
            if(diff[0] != 1) System.out.println(x);
            else{
                for(int i = 1; i<diff.length; i++){
                    if(diff[i] <2){
                        small = x-i;
                        big = x+i;
                        break;
                    }
                }
                if(arr.indexOf(small) > -1) System.out.println(big);
                else System.out.println(small);
            }
            //System.out.println(small+" "+big);

        }
        scan.close();

    }

    static ArrayList factors(int n ){
        ArrayList<Integer> facts = new ArrayList<>();
        for(int i = 1; i<=(int)Math.sqrt(n); i++){
            if(n%i == 0){
                if( i == Math.sqrt(n)) facts.add(i);
                else{
                    facts.add(i);
                    facts.add(n/i);
                }
            }
        }
        Collections.sort(facts);
        return facts;
    }

    static boolean isPrime (int n){
        if(factors(n).size() ==2) return true;
        else return false;
    }





    static long GCD(long a, long b) {
        // Everything divides 0
        if (a == 0) return b;
        if (b == 0) return a;

        // base case
        if (a == b) return a;

        // a is greater
        if (a > b) return GCD(a-b, b);
        return GCD(a, b-a);
    }
    static long LCM(long a, long b){
        return (a*b)/(GCD(a,b));
    }
    static String rev(String s){
        char[] arr = s.toCharArray();
        for(int i = 0; i<(s.length()+1)/2; i++){
            char temp = arr[i];
            arr[i] = arr[s.length()-i-1];
            arr[s.length()-i-1] = temp;
        }
        String fin = new String(arr);
        return fin;
    }
    static long pow(long a, long N) {
        if (N == 0) return 1;
        else if (N == 1) return a;
        else {
            long R = pow(a,N/2);
            if (N % 2 == 0) {
                return R*R;
            }
            else {
                return R*R*a;
            }
        }
    }

    static long powMod(long a, long N) {
        if (N == 0) return 1;
        else if (N == 1) return a % mod;
        else {
            long R = powMod(a,N/2) % mod;
            R *= R;
            R %= mod;
            if (N % 2 == 1) {
                R *= a;
                R %= mod;
            }
            return R % mod;
        }
    }

}