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";
    
const main = arg => {
    arg = arg.trim().split("\n");
    const N = parseInt(arg[0].split(" ")[0]);
    const X = parseInt(arg[0].split(" ")[1]);
    const numbers = arg[1].split(" ").map(n=>parseInt(n));
    
    const evenOdd = numbers.filter(n=>n % 2 === 0).length;
    
    if(N === 1) {
        console.log(numbers[0] - X);
        return;
    }
    
    if(evenOdd === 0 !== N && evenOdd !== 0) {
        console.log(1);
        return;
    }
    
    let answer = Math.abs(numbers[0] - X);
    
    for(let i=1; i<N; i++) {
        let temp = Math.abs(numbers[i] - X);
        
        if(temp < answer) {
            answer = temp;
        }
    }
    
    console.log(answer);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));