Problem:
Score : 300 points

Problem Statement

There are N cities on a number line. The i-th city is located at coordinate x_i.

Your objective is to visit all these cities at least once.

In order to do so, you will first set a positive integer D.

Then, you will depart from coordinate X and perform Move 1 and Move 2 below, as many times as you like:

Move 1: travel from coordinate y to coordinate y + D.

Move 2: travel from coordinate y to coordinate y - D.

Find the maximum value of D that enables you to visit all the cities.

Here, to visit a city is to travel to the coordinate where that city is located.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq X \leq 10^9

1 \leq x_i \leq 10^9

x_i are all different.

x_1, x_2, ..., x_N \neq X

Input

Input is given from Standard Input in the following format:

N X
x_1 x_2 ... x_N

Output

Print the maximum value of D that enables you to visit all the cities.

Sample Input 1

3 3
1 7 11

Sample Output 1

2

Setting D = 2 enables you to visit all the cities as follows, and this is the maximum value of such D.

Perform Move 2 to travel to coordinate 1.

Perform Move 1 to travel to coordinate 3.

Perform Move 1 to travel to coordinate 5.

Perform Move 1 to travel to coordinate 7.

Perform Move 1 to travel to coordinate 9.

Perform Move 1 to travel to coordinate 11.

Sample Input 2

3 81
33 105 57

Sample Output 2

24

Sample Input 3

1 1
1000000000

Sample Output 3

999999999

Solution in PHP7 (7.0.15) (judge verdict: Accepted)

<?php

$args = [];
$input = explode(' ', trim(fgets(STDIN)));

$n = (int)$input[0];
$x = (int)$input[1];

while(true){
	$input = explode(' ', trim(fgets(STDIN)));
	foreach ($input as $value) {
		if ($value !== '') {
			$args[] = (int)$value;
			++$cnt;
		}
		if (count($args) >= $n) {
			break;
		}
	}
	if (count($args) >= $n) {
		break;
	}
}

$args[] = $x;
sort($args);
$diff_array = [];
$length = count($args);
for ($i=1; $i < $length; $i++) { 
	$diff_array[] = $args[$i] - $args[$i-1];
}
$diff_array = array_unique($diff_array, SORT_NUMERIC);
sort($diff_array);
$min = $diff_array[0];

for ($i=$min; $i > 0; $i--) { 
	$flg = true;
	foreach ($diff_array as $value) {
		if ($value % $i !== 0) {
			$flg = false;
			break;
		}
	}
	if ($flg) {
		echo $i;
		break;
	}
}