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: Runtime Error)


module Main where

import Debug.Trace

main :: IO ()
main = do
  [a, _] <- map read . words <$> getLine
  s <- map read . words <$> getLine
  --a `traceShow`
  --(take 10 $ iterate (+1) 0) `traceShow`
  print $ solve a s

solve :: Int -> [Int] -> Int
solve a s = check a s (take 110 $ iterate (+1) 0)


check :: Int -> [Int] -> [Int] -> Int
check a s (p:ps)
  | a - p >= 1   && not (a - p `elem` s) = a - p
  | a + p <= 100 && not (a + p `elem` s) = a + p
  | otherwise = check a s ps