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: Accepted)

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <limits.h>

#define ROOP(i,n) for(i=0;i<n;i++)

//prototype declaration
int getint();
long long getllint();
double getdint();
char getch();
void setstring(char *s);
void showint(int i);
void showllint(long long i);
void showdouble(double i);
void showchar(char c);
void showstring(char *s);

int myPower(int a, int n) { // aのn乗の計算
	int x = 1;
	while (n > 0) { // 全てのbitが捨てられるまで
		if ( n & 1) { // 一番右のbitが１のとき
			x *= a;
		}
		a *= a;
		n >>= 1; // bit全体を右に1つシフトして一番右を捨てる
	}
	return x;
}

int min(int a, int b) {
	return a < b ? a : b;
}

int gdc(int a, int b) {
	if (a == 0 || b == 0) {
		return a + b;
	}
	if (a > b) {
		return gdc(a%b, b);
	} else {
		return gdc(a, b%a);
	}
}

int main(void) {
	int n, i, j;
	int X;
	n = getint();
	X = getint();
	int x[n];
	int diff[n];
	ROOP(i, n) {
		x[i] = getint();
		diff[i] = abs(x[i] - X);
	}

	int a, b;
	a = diff[0];
	for(i = 1; i < n; i++) {
		b = diff[i];
		a = gdc(a, b);
	}
	showint(a);
	return 0;
}

int getint() {
	int i;
	scanf("%d", &i);
	return i;
}

long long getllint() {
	long long i;
	scanf("%lld", &i);
	return i;
}

double getdint() {
	double i;
	scanf("%lf", &i);
	return i;
}

char getch() {
	char c;
	scanf("%c", &c);
	return c;
}

void setstring(char *s) {
	scanf("%s", s);
}

void showint(int i) {
	printf("%d\n", i);
}

void showllint(long long i) {
	printf("%lld\n", i);
}

void showdouble(double i) {
	printf("%lf\n", i);
}

void showchar(char c) {
	printf("%c\n", c);
}

void showstring(char *s) {
	printf("%s\n", s);
}