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)

#![allow(dead_code,unused_variables,unused_imports)]
use proconio::{fastout, input};
use proconio::marker::Chars;
use std::cmp::{max,min};
use std::collections::HashSet;

#[fastout]
fn main() {
    input!{
        x:i32,
        n:usize,
        p:[usize;n],
    }
    
    let mut st : HashSet<usize> = HashSet::new();
    for e in p{
        st.insert(e);
    }
    let mut ans = 103;
    let mut d = 200;
    for i in 0..=101{
        if !st.contains(&i){
            if (x-i as i32).abs() < d{
                ans = i;
                d = (x-i as i32).abs();
            }
        }
    }
    println!("{}",ans);
}

fn lower_bound(x: &Vec<usize>, key:usize) -> usize{
    let mut l = 0;
    let mut r = x.len();

    while l+1 < r{
        let mid = (r-l)/2 + l;

        if key < x[mid]{
            r = mid;
        }else{
            l = mid;
        }
    }
    l
}