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: Wrong Answer)

use proconio::input;

fn main() {
    input! {
        x: usize,
        n: usize,
        mut p: [usize; n],
    }

    solve(x, &mut p);
}

fn solve(x: usize, p: &mut [usize]) {
    p.sort();

    match p.binary_search(&x) {
        Err(_) => {
            println!("{}", x);
            return;
        }
        Ok(_) => {}
    }
    let mut min = 0;
    let mut max = 100;
    for i in 0..101 {
        if i < x {
            match p.binary_search(&i) {
                Ok(_) => continue,
                Err(_) => min = i,
            }
        }
        if i > x {
            match p.binary_search(&i) {
                Ok(_) => continue,
                Err(_) => {
                    max = i;
                    break;
                }
            }
        }
    }
    if x - min <= max - x {
        println!("{}", min);
    } else {
        println!("{}", max);
    }
}