C - Skip

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.

3 3
1 7 11

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 $11$.

3 81
33 105 57

24

1 1
1000000000

999999999