Recently, Kozak Vus found a chip and n points that are on the same line. The chip initially has the coordinate x, and the i-th point has the coordinate ai.
Cossack Mustache can first choose any positive integer k. After that, change the chip's coordinate any number of times, adding or subtracting k from it, that is, move the chip in any of the two directions by a distance of k.
Kozak Vus is interested: at what maximum value of k will the chip be able to visit all n given points.
The first line contains two integers n and x (2≤n≤105,−1018≤x≤1018) — the number of points on the line and the initial coordinate of the chip.
The second line contains n integers a1,a2,…,an (−1018≤ai≤1018) — coordinates of chips.
It is guaranteed that all numbers of the array a are pairwise different.
Output one number — the maximum value of k at which the chip will be able to visit all n given points.
If your solution will work correctly for n,∣ai∣≤100, then it will score at least 30 points.