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 PHP (7.4.4) (judge verdict: Accepted)

<?php

fscanf(STDIN, "%d %d", $x, $n);
if ($n == 0) { echo $x, PHP_EOL; return; }

$P = array_map('intval', explode(' ', trim(fgets(STDIN))));
sort($P);

$rp = [];
for ($i = 0; $i >= -100; --$i) {
    $rp[] = $i;
}
for ($i = 1; $i <= 200; ++$i) {
    if (!in_array($i, $P)) {
        $rp[] = $i;
    }
}
$rp[] = PHP_INT_MAX;
sort($rp);

if (in_array($x, $rp)) {
    echo $x, PHP_EOL;
    return;
}

$l = 0;
$r = count($rp);
while ($r - $l >= 1) {
    $mid = intdiv($r + $l, 2);
    if ($rp[$mid] > $x) {
        $r = $mid;
    } else {
        $l = $mid + 1;
    }
}

if (abs($x - $rp[$r]) == abs($x - $rp[$r - 1])) {
    echo $rp[$r - 1], PHP_EOL;
} else if (abs($x - $rp[$r]) > abs($x - $rp[$r - 1]) ) {
    echo $rp[$r - 1], PHP_EOL;
} else {
    echo $rp[$r], PHP_EOL;
}