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 Python (3.8.2) (judge verdict: Accepted)

import math
import sys

x, n = map(int, input().split())

if n == 0:
    print(x)
    sys.exit()

p = list(map(int, input().split()))

p.sort()
# closest
ans = min(p, key=lambda y:abs(y-x))
idx = p.index(min(p, key=lambda y:abs(y-x)))

# print(p)
# print(ans, idx)

if x != ans:
    print(x)
    sys.exit()


cnt = idx
larger_near = p[cnt]
smaller_near = p[cnt]

while cnt < n:
    tmp = p[cnt]
    cnt += 1
    if cnt == n:
        larger_near = tmp + 1
        break
    elif p[cnt] != tmp + 1:
        larger_near = tmp + 1
        break

cnt = idx
while cnt >= 0:
    tmp = p[cnt]
    cnt -= 1
    if p[cnt] != tmp - 1:
        smaller_near = tmp - 1
        break

if abs(smaller_near - x) <= abs(larger_near - x):
    ans = smaller_near
else:
    ans = larger_near
print(ans)