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 OCaml (4.10.0) (judge verdict: Wrong Answer)

(*
ocamlfind ocamlopt -package batteries -linkpkg main.ml -o a.out
*)
open Batteries

let x, n = Scanf.sscanf (read_line ()) "%d %d" ( fun x n -> x, n)
let lst = Str.split (Str.regexp " ") (read_line ())
          |> List.map int_of_string

let () = 
        let (ans, _) = 
                (
                        if lst = [] then
                                (x, 0)
                        else
                                let set = 
                                        (
                                                let max = List.max lst in
                                                let pset = List.range 0 `To max
                                                           |> Set.of_list in
                                                let sset = Set.of_list lst in
                                                        Set.diff pset sset 
                                        ) in
                                let lst = Set.to_list set in
                                        List.map (fun elmnt -> (elmnt, abs (elmnt - x))) lst 
                                        |> List.sort (fun (el1, diff1) (el2, diff2) -> compare diff1 diff2)
                                        |> List.hd
                ) in
                Printf.printf "%d\n" ans