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 Haskell (GHC 8.8.3) (judge verdict: Accepted)

{-# LANGUAGE PartialTypeSignatures #-}
module Main (main) where

import qualified Data.ByteString.Char8 as C8
import qualified Data.Char as C
import qualified Data.List as L

main :: IO ()
main = do
  [x,n] <- readInts
  readInts >>= output . solve (x,n)

solve :: (Int,Int) -> [Int] -> _
-- solve (x,0) _ = x
solve (x,_) xs = check $ zip [x,x-1..] [x..]
  where
    check ((y1,y2):ys)
      | y1 `elem` xs && y2 `elem` xs = check ys
      | y1 `elem` xs = y2
      | y2 `elem` xs = y1
      | otherwise = y1

output :: _ -> IO ()
output = print

-- utils
readInts :: IO [Int]
readInts = L.unfoldr (C8.readInt . C8.dropWhile C.isSpace) <$> C8.getLine