Kozak Vus and a chip#10356
Recently, Kozak Vus found a chip and points that are all located on the same straight line. The chip initially has coordinate , and the -th point has coordinate a_i.
Kozak Vus can first choose any positive integer . After that, he can change the chip's coordinate any number of times, by either adding or subtracting , that is, move the chip in either direction by a distance of .
Kozak Vus is interested in the following question: what is the largest value of such that the chip can visit all given points?
The first line contains two integers and (2 \le n \le 10^5, -10^{18} \le x \le 10^{18})—the number of points on the line and the initial coordinate of the chip.
The second line contains integers a_1, a_2, \dots, a_n (-10^{18} \le a_i \le 10^{18})—the coordinates of the points.
It is guaranteed that all a_i are pairwise distinct.
Output a single integer—the maximum value of such that the chip will be able to visit all given points.
Example 1
Example 2
Example 3
If your solution works correctly for n, |a_i| \le 100, you will receive at least points.