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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

use v5.18; # strict say state
use warnings;
use List::Util qw(reduce first max min sum0);

chomp (my ($n, $x) = split / /, <STDIN>);
chomp (my @y = split / /, <STDIN>);
my $d = max(@y, $x) - min(@y, $x);
my $gcd = sub {
  my ($x, $y) = @_;
  while ($y) {
    my $r = $x % $y;
    $r += $y if $r < 0;
    $x = $y;
    $y = $r;
  }
  return $x;
};
my $g = $x;
for my $i (0..$n-1) {
  $g = $gcd->($g, $y[$i]);
}
for my $i (1..$d) {
  next if $d%$i>0;
  my $cf = $x % ($d/$i);
  my $sf = 1;
  for my $j (@y) {
    $sf = 0 if $j % ($d/$i) != $cf;
  }
  if ($sf == 1) {
    say $d/$i if $sf == 1;
    exit;
  }
}