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: Runtime Error)

#include <bits/stdc++.h>
#define REP(i, n) for(int i = 0; i < n; i++)
#define FOR(i, m, n) for(int i = m; i < n; i++)
#define ll long long
#define MOD 1000000007
#define MAX 100010
#define aout(a) REP(i,sizeof(a)) cout << a[i] << " "; cout << endl;
#define vout(v) REP(i,v,size()) cout << v[i] << " "; cout << endl;
using namespace std;
using Graph = vector<vector<int>>;
#define PI 3.1415926535897932384
int N;
ll ans = 0;
bool flag = false;

int main(){
  int N; cin>>N;
  vector<int> A(N);
  REP(i,N) cin>>A[i];
  
  sort(A.begin(),A.end(),greater<>());
  REP(i,N){
    flag = false;
    FOR(j,i+1,N){
      if(A[i]%A[j] == 0){
        flag = true;
        break;
      }
    }
  	if(!flag) ans++;
  }
  if(A[N-2] == A[N-1]) ans--;
  cout << ans;
}