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(8)::n,x,p,i,q
	integer(8),allocatable::a(:)
	
	read*,n,x
	allocate(a(n))
	
	read*,a
	
	a = abs(a-x)
	p = a(1)
	
	if(n>1)then
	do i = 2,n
		call euc(p,a(i),q)
		p = q
	enddo
	endif
	
	print "(i0)",p
end program main

subroutine euc(a1,b1,c)
implicit None
integer(8)::a1,b1,c,a,b
	
	a =a1
	b =b1
	c =1
	
	do while (a /=0 .and. b /= 0)
		if (a > b)then
			c =b
			a =mod(a,b)
			else
			c =a
			b =mod(b,a)
		endif
	enddo
end subroutine euc