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)

/*2019/08/25 */
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include<string.h>
#define MOD 1000000007
#define MIN 999999999
#define MAX -999999999
#define llMIN 999999999999999
#define llMAX -99999999999999
typedef long long int ll;
typedef unsigned long long int ull;
void llswap(ll *x,ll *y){ll temp;temp=*x;*x=*y;*y=temp;}
void swap(int *x,int *y){int tmp;tmp=*x;*x=*y;*y=tmp;}
int rmax(int x,int y){return x>y?x:y;}
int rmin(int x,int y){return x>y?y:x;}
ll llrmax(ll x,ll y){return x>y?x:y;}
ll llrmin(ll x,ll y){return x>y?y:x;}
int asc(const void *a,const void *b){return *(int*)a-*(int*)b;}
int desc(const void *a,const void *b){return *(int*)b-*(int*)a;}
int llasc(const void *a,const void *b){return *(ll*)a-*(ll*)b;}
int lldesc(const void *a,const void *b){return *(ll*)b-*(ll*)a;}
int gcd(int x,int y){if(y==0)return x;if(x<y)swap(&x,&y);return gcd(y,x%y);}
/*
int asc_t(const void *a,const void *b){return ((struct_t*)a)->member - ((struct_t*)b)->member;}
int desc_t(const void *a,const void *b){return ((struct_t*)b)->member - ((struct_t*)a)->member;}
*/

int main(){
    int N,X,x[200000];
    int d[200000];
 
    scanf("%d %d",&N,&X);
    for(int i=0;i<N;i++){
        scanf("%d",&x[i]);
    }
    x[N]=X;
 
    qsort(x,N+1,sizeof(int),asc);
    int min=MIN,min_i;
    for(int i=1;i<=N;i++){
        d[i-1]=x[i]-x[i-1];
        if(min>x[i]-x[i-1]){
            min=x[i]-x[i-1];
            min_i=i-1;
        }
    }
    int x1,y1,tmp;
    int max_gcd=MAX;
    for(int i=0;i<N;i++){
        if(min_i==i)continue;
        if(max_gcd<gcd(d[i],min)){
            max_gcd=gcd(d[i],min);
        }
    }
    printf("%d\n",max_gcd);
    return 0;

}