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: Runtime Error)

function Getnum(number1,number2)
	local intTemp=1;
	if number2 < number1 then
		intTemp=number2;
		number2=number1;
		number1=intTemp;
	end
	while(number1~=0) do
		intTemp =number2 % number1;
		number2=number1;
		number1=intTemp;
	end
	return number2;
end

local n = io.read()
local x = io.read()
local s = {}
local sum = s[1]
for i=1,n do
	a = io.read()
	s[i] = a>x and a-x or x-a
end

for i=1,n-1 do
	sum = Getnum(sum,s[i+1])
end

print(sum)
--#17025109 | kachidoki's solution for [AtCoder-4255] [Problem C]