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 Python (3.4.3) (judge verdict: Wrong Answer)

import numpy as np
def div(N):
    sq = int(np.sqrt(N))
    divs = [1]
    for i in range(2,sq+1):
        if  N%i == 0:
            divs.append(i)
    divs.append(N)
    return divs


N,S = map(int, input().split())
X = list(map(int,input().split()))

X.append(S)
X = sorted(X)

X_del = []
for i in range(N):
    X_del.append(X[i+1] - X[i])

min_del = min(X_del)
ans = 1

np_X_del = np.array(X_del)
divs = div(min_del)

for div in divs[::-1]:
    sa = abs(np_X_del - div)
    if np.min(sa) >= 0:
        waru = np_X_del % div

        if np.max(waru) == 0:
            print(div)
            exit()