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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

'use strict';

function Main(input) {
  const N = Number(input.split('\n')[0].split(' ')[0]);
  const X = Number(input.split('\n')[0].split(' ')[1]);

  let Xlist = [];

  for(let i=0; i<N; i++) {
    Xlist.push(Math.abs(Number(input.split('\n')[1].split(' ')[i]) - X));
  }
  
  const gcd = (m, n) => {
    if(n === 0) {
      return m;
    } else {
      return gcd(n, m % n);
    }
  }

  if(Xlist.length === 1) {
    console.log(Xlist[0] - X);
  } else {
    let gcdans = gcd(Xlist[0], Xlist[1]);
    for(let k=1; k<N-1; k++) {
      gcdans = gcd(gcdans, Xlist[k]);
    }

    console.log(gcdans);
  }


};

Main(require("fs").readFileSync("/dev/stdin", "utf8").trim());