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 test
integer(8)::n, x, ans, i, t, k, p, a
allocatable::a(:)
read(*,*)n, x
allocate(a(n))
read(*,*)(a(i), i=1,n)
 
if(n==1)then
t=a(1)-x
ans=abs(t)
 
else
t=x-a(1)
ans=abs(t)
 
do i=1,n
t=x-a(i)
k=abs(t)
call subr4(ans,k,p)
ans=p
end do
end if
write(*,*)ans
 
end program test
 
subroutine subr4(a,b,q)
  implicit none
  integer(8) :: a, b, q
  integer(8) :: m, n, k
  ! step 1
  m = a
  n = b
  do
     ! step 2
     k = mod(m, n)
     ! step 3
     if (k == 0) then
        q=n
        exit
     end if
     ! step 4
     m = n
     n = k
  end do
 end subroutine subr4