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>

std::vector<unsigned long> memo(200), deleted(200), visited(200);

unsigned long dfs(unsigned long X, unsigned long x){
    if(memo[x])return memo[x] - 1;
    if(visited[x])return 100000;
    visited[x] = 1;
    if(!deleted[x])return x;
    unsigned long up{dfs(X, x + 1)}, down{dfs(X, x - 1)};
    unsigned long ret{up + down < 2 * X ? up : down};
    return (memo[x] = ret + 1) - 1;
}

int main(){
    using namespace std;
    unsigned long X, N;
    cin >> X >> N;
    for(unsigned long i{0}, p; i < N; ++i){
        cin >> p;
        deleted[p] = 1;
    }
    cout << dfs(X, X) << endl;
    return 0;
}