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: Wrong Answer)

<?php
fscanf(STDIN, "%d %d", $max, $start);
$cities = trim(fgets(STDIN));
$cities = explode( " ", $cities );
rsort($cities);

if( $max == 1 )
{
  echo abs($cities[0]- $start);
  die;
}

if( $cities[0] > $start )
{ array_unshift($cities, $start); }
elseif( $cities[$max-1] < $start )
{ $cities[] = $start; }

  


for( $i=1; $i<$max; $i++ )
{
  if( $cities[$i-1] < $start && $start < $cities[$i] )
  {
    $distances[] = $cities[$i-1] - $start;
    $distances[] = $start - $cities[$i];
  }
  else
  { $distances[] = $cities[$i-1] - $cities[$i]; }
}

$distances = array_unique($distances);
$distances = array_values($distances);
sort($distances);

$step = $distances[0];
$count = count($distances);
$result = false;
while( !$result )
{
  $result = true;
  for( $i=0; $i<$count; $i++  )
  {
    if( $distances[$i] % $step != 0 )
    {
      break;
    }
  }

  if( $i < $count )
  {
    $result = false;
    $step = floor( $step/2 );
  }
}

echo $step;