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++ (Clang 10.0.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

int main() {
    int X, N;
    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());

    int min = 100000000, min_index;
    for (int i = 0; i < N; ++i) {
        int _min = abs(X - p[i]);
        if (_min < abs(X - min)) {
            min = p[i];
            min_index = i;
        }
    }

    int res;
    int min_plus = min + 1;
    int min_plus_index = min_index + 1;
    int min_minus = min - 1;
    int min_minus_index = min_index - 1;
    while (true)
    {
        if (min_minus != p[min_minus_index]) {
            res = min_minus;
            break;
        }
        min_minus -= 1;
        min_minus_index -= 1;
        
        if (min_plus != p[min_plus_index]) {
            res = min_plus;
            break;
        }
        min_plus += 1;
        min_plus_index +=1;
    }

    cout << res << endl;

}