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 Rust (1.15.1) (judge verdict: Wrong Answer)

fn main () {
    let mut nx = String::new();
    let mut xi = String::new();
    std::io::stdin().read_line(&mut nx).unwrap();
    std::io::stdin().read_line(&mut xi).unwrap();
    let nx: Vec<usize> = nx.trim().split_whitespace().flat_map(str::parse).collect();
    let mut xi: Vec<usize> = xi.trim().split_whitespace().flat_map(str::parse).collect();
    xi.push(nx[1]);
    xi.sort();
    let mut diff: Vec<usize> = xi.iter().zip(xi.iter().skip(1)).map(|(&a, &b)| if a > b { a - b } else { b - a }).collect();
    diff.sort();
    let pa = diff[0];
    let pa2 = diff.iter().filter(|&a| diff.iter().all(|&b| b % a == 0)).last();

    println!("{}", pa2.unwrap_or(&1));
}