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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program main
implicit none
integer :: i, g
integer :: n, m
integer , allocatable :: x(:)

read(*,*) n, m
allocate( x(n) )
read(*,*) x(1:n)
x = abs(x -m)
if( n == 1 ) then
   write(*,'(i0)') x(1)
else
   do i = 1, n-1
      call gcdlcm(x(i), x(i+1), g)
      x(i+1) = g
   end do
   write(*,'(i0)') g
end if

stop
contains
  subroutine gcdlcm( a, b, g )
    integer , intent(in)  :: a, b
    integer , intent(out) :: g

    integer :: i, j, k,l

    i = a
    j = b
    do while( j /= 0 )
       k = mod(i,j)
       i = j
       j = k
    end do
    g = i
    l = a*b/g
  end subroutine gcdlcm

end program main