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);
	input!(n: usize);

	if n == 0 {
		println!("{}", x);
		return;
	}

	input!(p: [usize; n]);
	let mut p = p;
	p.sort(); 

	let r = p.binary_search(&x);
	match r {
		Err(_) => {
			println!("{:?}", r);
			println!("{}", x);
			return;
		},
		_ => (),
	}

	for i in 1..100 {
		let r = p.binary_search(&(x-i));
		match r {
			Err(_) => {
				println!("{}", x-i);
				return;
			},
			_ => (),
		}
		let r = p.binary_search(&(x+i));
		match r {
			Err(_) => {
				println!("{}", x+i);
				return;
			},
			_ => (),
		}
	}
}