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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Data.List
factor 1 = [1]
factor x = reverse $sort $nub $1:inFactor [] [1] 2 x
 where
  inFactor fadd all begin x
   | x == begin       = fadd++(x:map (*begin) all)
   | mod x begin == 0 = let bye = begin:map (*begin) all in inFactor (fadd++bye)  bye begin (div x begin)
   | otherwise        = inFactor fadd all (begin+1) x
-- factor x = x:[y|y<-[div x 2,div x 2 -1..1],mod x y == 0]

check [1] _ = 1
check (x:xs) list = if null (filter ((0/=) . flip mod x) list) then x else check xs list

main = do
 [n,x] <- map read . words <$> getLine :: IO [Int]
 xs <- map read. words <$> getLine
 let list = map (flip(-)(minimum (x:xs))) $ sort (x:xs)
 print $ check (factor (head $ tail list)) $ drop 2 list