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: Runtime Error)

X,N = map(int, input().split())
p = list(map(int, input().split()))
p = sorted(p)
for i in p:
    if i in lista:
        lista.remove(i)
def binary_search_find_closest(data, target):
    if len(data) == 0:
        return None
    if len(data) == 1:
        return data[0]
    min_diff = float('inf')
    imin = 0
    imax = len(data) - 1
    closest_num = None
    while imin <= imax:
        imid = imin + (imax - imin) // 2
        #　中心の左右の値と目標との差を計算する。
        if imid + 1 < len(data):
            min_diff_right = abs(data[imid+1] - target)
        if imid > 0:
            min_diff_left = abs(data[imid-1] - target)
        # 最初の差と最も最小に近い値を更新する。
        if min_diff_left < min_diff:
            min_diff = min_diff_left
            closest_num = data[imid-1]
        if min_diff_right < min_diff:
            min_diff = min_diff_right
            closest_num = data[imid+1]
        # 2分探索する。
        if data[imid] < target:
            imin = imid + 1
        elif data[imid] > target:
            imax = imid -1
        else:
            return data[imid]
    return closest_num
binary_search_find_closest(lista,X)