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 PyPy3 (7.3.0) (judge verdict: Accepted)

def binarySearch (arr, l, r, x): 
  
    # Check base case 
    if r >= l: 
  
        mid = l + (r - l) // 2
  
        # If element is present at the middle itself 
        if arr[mid] == x: 
            return mid 
          
        # If element is smaller than mid, then it  
        # can only be present in left subarray 
        elif arr[mid] > x: 
            return binarySearch(arr, l, mid-1, x) 
  
        # Else the element can only be present  
        # in right subarray 
        else: 
            return binarySearch(arr, mid + 1, r, x) 
  
    else: 
        # Element is not present in the array 
        return -1

l=list(map(int, input().split(' ')))

find=l[0]
n=l[1]

if n==0:
    print(find)
else:
    l=list(map(int, input().split(' ')))
    l=sorted(l)

    a=find
    b=find
    
    while True:
        if binarySearch(l, 0, n-1, b)==-1:
            print(b)
            break
        elif binarySearch(l, 0, n-1, a)==-1:
            print(a)
            break
        else:
            a+=1
            b-=1