Problem: 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.

Examples

Input

3 3
1 7 11


Output

2


Input

3 81
33 105 57


Output

24


Input

1 1
1000000000


Output

999999999

Solution (in CPP):

Solution:
#include<stdio.h>
#define fo(i,a,b) for(int i=a;i<=b;i++)
int n,X,D,x;
inline int gcd(int a,int b){
	if (b==0) return a;
	return gcd(b,a%b);
}
int main(){
	scanf("%d%d%d",&n,&X,&x);
	D=x-X;
	if (D<0) D=-D;
	fo(i,2,n){
		scanf("%d",&x);
		x-=X;
		if (x<0) x=-x;
		D=gcd(x,D);
	}
	printf("%d\n",D);
	return 0;
}