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: Wrong Answer)

implicit none
integer :: n,x0
integer,allocatable :: x(:)
integer :: i,p,q,r,gcd

read *,n,x0
allocate(x(n))
read *,(x(i),i=1,n)

do i = 1, n
   x(i) = abs(x(i) - x0)
enddo

gcd = x(1)
do i = 2, n
   p = min(gcd,x(i))
   q = max(gcd,x(i))
   
   r = 1
   do while (r > 0)
      r = mod(q,p)
      q = p
      p = r
   enddo
   
   if (i == 2 .or. q > gcd) then
      gcd = q
   endif
enddo

write(*,'(i0)') gcd
end