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)

use std::cmp::min;

fn read<T: std::str::FromStr>(
    stdin_lock: &mut std::io::StdinLock,
    buf: &mut Vec<u8>,
    delimiter: u8,
) -> T {
    buf.clear();
    let l = std::io::BufRead::read_until(stdin_lock, delimiter, buf).unwrap();
    buf.truncate(l - 1); // remove delimiter
    let s = unsafe { std::str::from_utf8_unchecked(&buf) };
    s.parse().unwrap_or_else(|_| panic!("read"))
}

fn gcd(a: i32, b: i32) -> i32 {
    fn gcd1(m: i32, n: i32) -> i32 {
        if n == 0 {
            m
        } else {
            gcd1(n, m % n)
        }
    }
    if a > b {
        gcd1(a, b)
    } else {
        gcd1(b, a)
    }
}

fn main() {
    let stdin = std::io::stdin();
    let mut stdin_lock = stdin.lock();
    let mut buf: Vec<u8> = Vec::new();
    let n: usize = read(&mut stdin_lock, &mut buf, b' ');
    let x: i32 = read(&mut stdin_lock, &mut buf, b'\n');
    let mut xv = vec![0i32; n];
    for i in 0..n - 1 {
        xv[i] = read(&mut stdin_lock, &mut buf, b' ');
    }
    xv[n - 1] = read(&mut stdin_lock, &mut buf, b'\n');

    let mut ans = (x - xv[0]).abs();
    for i in 1..n {
        ans = min(ans, (x - xv[i]).abs());
    }
    for i in 1..n {
        ans = gcd(ans, xv[i] - xv[i - 1]);
    }
    println!("{}", ans);
}