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 Ruby (2.3.3) (judge verdict: Accepted)

n,x=gets.chomp.split(" ").map(&:to_i)
d=gets.chomp.split(" ").map(&:to_i).map{|a|(a-x).abs}.sort
ans=0
max_d=d.min
stop=false
@yaku_arr=[]
def yaku(num)
  n=1
  while n**2<num do
    if num%n==0 then
      @yaku_arr.push(n,num/n)
    end
    n+=1
  end
  return @yaku_arr.sort.reverse
end
a=yaku(max_d)

k=1
while !stop do
  for i in 0..(n-1) do
    stop=true
    if d[i]%max_d!=0 then
      stop=false
      break
    end
  end
  if !stop then
    max_d=a[k]
    k+=1
  end
end
p max_d