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 Lua (5.3.2) (judge verdict: Wrong Answer)

local split_space = function(str)
  words = {}
  for word in str:gmatch("%w+") do
    table.insert(words, tonumber(word))
  end
  return words
end

gcd = function(a, b)
  if b ~= 0 then
    return gcd(b, a % b)
  else
    return math.abs(a)
  end
end

local nx = split_space(io.read("*l"))
local data = split_space(io.read("*l"))
if #data == 1 then
  print(data[1] - 1)
  os.exit(0)
end
table.insert(data, nx[2])
table.sort(data)
local ans = 0
local diff = {}
for i=1, #data-1 do
  local d1 = data[i+1] - data[i]
  table.insert(diff, d1)
end
ans = gcd(diff[1], diff[2])
for i=3, #diff do
  local tmp = gcd(ans, diff[i])
  if tmp > ans then
    ans = tmp
  end
end
print(ans)