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 BangPatterns #-}
import           Control.Exception           (assert)
import           Control.Monad
import           Control.Monad.Primitive
import qualified Control.Monad.ST            as ST
import qualified Data.Array.IO               as IO
import qualified Data.Array.ST               as ST
import qualified Data.Array.Unboxed          as A
import           Data.Bits
import qualified Data.ByteString.Char8       as BS
import           Data.Char
import           Data.Foldable
import           Data.List
import qualified Data.Map.Strict             as Map
import           Data.Maybe
import qualified Data.Sequence               as Seq
import qualified Data.Set                    as Set
import qualified Data.Vector                 as VB
import qualified Data.Vector.Mutable         as VBM
import qualified Data.Vector.Unboxed         as V
import qualified Data.Vector.Unboxed.Mutable as VM
import           Debug.Trace

readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine
getIntVec n = V.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine

readInteger = fst . fromJust . BS.readInteger
readIntegerList = map readInteger . BS.words
getInteger = readInteger <$> BS.getLine
getIntegerList = readIntegerList <$> BS.getLine

inf :: Int
inf = 10^18

main = do
  [x, n] <- getIntList
  ps <- getIntList

  v <- VM.new 102
  VM.set v False
  forM_ ps $ \i -> VM.write v i True

  let solve :: Int -> IO Int
      solve i = do let x1 = x - i
                       x2 = x + i
                   c1 <- VM.read v x1
                   c2 <- VM.read v x2
                   if c1 == False
                     then return x1
                     else if c2 == False
                          then return x2
                          else solve (i+1)

  ans <- solve 0

  print ans