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 Julia (0.5.0) (judge verdict: Accepted)

function parseInt(x) parse(Int, x) end

function gcd(x,y)
	r = x%y
	while r > 0
		temp = r
		r = y%r
		y = temp
	end
	return(y)
end

function main()
	n = parseInt.(split(readline()))
	x = parseInt.(split(readline()))
	if n[1] == 1
		print(abs(x[1]-n[2]))
	else
		y = [0 for i in 1:n[1]]
		for i in 1:n[1]
			y[i] = abs(x[i]-n[2])
		end
		gcdd = gcd(y[1],y[2])
		if n[1] >= 3
			for i in 3:n[1]
				gcdd = gcd(gcdd, y[i])
			end
		end
		print(gcdd)
	end
end

main()