Kozak Vus and a chip

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 $a_i$.

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.

Input

The first line contains two integers $n$ and $x$ ($2\le n\le 10^5,-10^{18}\le x\le 10^{18}$) — the number of points on the line and the initial coordinate of the chip.

The second line contains $n$ integers $a_1,a_2,\dots ,a_n$ ($-10^{18}\le a_i\le 10^{18}$) — coordinates of chips.

It is guaranteed that all numbers of the array $a$ are pairwise different.

Output

Output one number — the maximum value of $k$ at which the chip will be able to visit all $n$ given points.

Examples

Scoring

If your solution will work correctly for $n,|a_i|\le 100$, then it will score at least $30$ points.