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: Wrong Answer)

#!/usr/bin/perl

my ($N,$X) = map {$_ - 0} split(/\s+/o,<STDIN>);
my @x = map { abs(($_ - 0) - $X) } split(/\s+/o,<STDIN>);
my $D = 10 ** 10;
for(my $i=0;$i<$N;$i++){
  $D = $x[$i] if $x[$i] != 0 and $x[$i] < $D;
}
foreach my $x (@x){
  next if $x == 0;
  my $nD = &gcd($x,$D);
}
print "$D\n";
exit(0);

sub gcd {
  my $mm = shift;
  my $nn = shift;
  while($nn != 0){
    my $rr = $mm % $nn;
    $mm = $nn;
    $nn = $rr;
  }
  return $mm;
}