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)

function gcd(a, b) {
    if (b === 0)
        return a;

    return gcd(b, a % b);
}

function main(arg) {
    arg = arg.split("\n")
    var tmp = arg[0].split(" ")
    var N = tmp[0]
    var X = tmp[1]
    var xi = arg[1].split(" ")
    
    xi.push(X)
    xi = xi.map(function(e){return parseInt(e,10)})
    
    xi.sort(function(a,b) {
        if (a > b) {
            return 1
        }
        return -1
    })
    
    if (xi.length === 2) {
        console.log(xi[1] - xi[0])
        return
    }
    
    
    var result = []
    
    for (var i = 1; i < xi.length; i++ ){
        result.push(xi[i] - xi[i-1])
    }
    
    result = result.filter(function (x, i, self) {
        return self.indexOf(x) === i;
    });
    
    if (result.length === 1) {
        console.log(result[0])
        return
    } else {
        while(1) {
            var _tmp = [];
            result = result.sort(function(a,b) {
                if (a > b) {
                    return 1
                }
                return -1
            })

            for (var i = 1; i < xi.length; i++ ){
                _tmp.push(result[i] - result[i-1])
            }

            _tmp = _tmp.filter(function (x, i, self) {
                return self.indexOf(x) === i;
            });
            result = _tmp
            if (result.length === 1) {
                break;
            } else{
                result = _tmp
            }
        }
        console.log(result[0])
    }
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));