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 Rust (1.42.0) (judge verdict: Accepted)

use proconio;
use std::collections::VecDeque;

#[proconio::fastout]
fn main() {
    proconio::input! {
        x: i64,
        n: usize,
        mut pp: [i64; n],
    }

    pp.sort_by(|l, r| {
        let ld = (x - l).abs();
        let rd = (x - r).abs();
        ld.cmp(&rd).then(l.cmp(r))
    });
    let mut pp: VecDeque<_> = pp.into();
    // println!("{:?}", pp);

    let mut v: Vec<i64> = vec![];
    v.push(x);
    for i in 1..=100 {
        v.push(x - i);
        v.push(x + i);
    }
    let mut v: VecDeque<_> = v.into();
    // println!("{:?}", v);

    let mut result = x;
    while v.len() > 0 {
        result = v[0];
        let in_pp = pp.iter().any(|p| p == &result);
        if in_pp {
            // println!("{} is in pp", result);
            v.pop_front();
            pp.pop_front();
            continue;
        }
        // println!("{} is NOT in pp", result);
        break;
    }
    println!("{}", result);
}