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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<string.h>
#include<stdlib.h>

int max(int a, int b){
  if(a > b) return a;
  else return b;
}

long long int min(long long int a, long long int b){
  if(a < b) return a;
  else return b;
}

int sort(const void *a, const void *b){
  return *(int*)a - *(int*)b;
}

int gcd(int a, int b){
  if(a % b ==  0) return b;
  else gcd(b, a%b);

}

int main(){

  int n,x;
  scanf("%d %d",&n,&x);

  int city[100001];
  for(int i = 0; i < n; ++i){
    scanf("%d",&city[i]);
  }

  city[n] = x;
  qsort(city, n+1, sizeof(int), sort);

  int difference[100001];
  for(int i = 0; i < n; ++i){
    difference[i] = city[i+1] -city[i];
  }

  qsort(difference, n, sizeof(int), sort);

  int ans = 0;
  int tmp = difference[0];
  for(int i = 0; i < n; ++i){
    tmp = gcd(tmp,difference[i]);
    ans = max(ans,tmp);
  }

  printf("%d",ans);

  return 0;

}