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 OCaml (4.02.3) (judge verdict: Accepted)

open Printf open Scanf
module MyInt = struct let (+) = (+) let (-) = (-) let (/) = (/) let ( * ) = ( * ) let (mod) = (mod) let (%) = (mod) let (+=) r v = r := !r + v let (-=) r v = r := !r - v let ( *=) r v= r := !r * v let (/=) r v = r := !r / v end
module MyInt64 = struct
	let (+$) = (+) let (-$) = (-) let (/$) = (/) let ( *$) = ( * ) let (+) p q = Int64.add p q let (-) p q = Int64.sub p q let ( * ) p q = Int64.mul p q let (/) p q = Int64.div p q let (+=) r v = r := !r + v let (-=) r v = r := !r - v let ( *=) r v= r := !r * v let (/=) r v = r := !r / v let labs p = if p < 0L then -1L*p else p let (~|) p = Int64.to_int p let (~~|) p = Int64.of_int p let input_i64_array n = Array.init (~| n) (fun _ -> Scanf.scanf " %Ld" (fun v -> v)) let get_i64 _ = Scanf.scanf " %Ld" (fun v -> v) let get_2_i64 _ = Scanf.scanf " %Ld %Ld" (fun u v -> u,v) let get_3_i64 _ = Scanf.scanf " %Ld %Ld %Ld" (fun u v w -> u,v,w) let get_4_i64 _ = Scanf.scanf " %Ld %Ld %Ld %Ld" (fun u v w x -> u,v,w,x) let get_5_i64 _ = Scanf.scanf " %Ld %Ld %Ld %Ld %Ld" (fun u v w x y -> u,v,w,x,y) let print_i64_endline n = n |> Int64.to_string |> print_endline let (mod) m n = m - (m/n) * n let (%) = (mod) let rec gcd m n = match m,n with | m,0L -> m | m,n -> gcd n (m mod n) let lcm m n = (m*n) / gcd m n let rep from_ to_ fbod = let i,f = ref ~|from_,ref true in while !i <= ~|to_ && !f do match fbod ~~| !i with | `Break -> f := false | _ -> i := !i +$ 1; done
	let string_of_list ?(separator=" ") f ls = let rec f0 a s = match a with | [] -> s | [h] -> s ^ (f h) ^ separator | h::t -> f0 t (s ^ (f h) ^ separator) in f0 ls "" let char_list_of_string str = let rec f0 i a = if i<0 then a else f0 (i-$1) (str.[i]::a) in f0 (String.length str -$ 1) [] let string_of_char_list ls = List.fold_left (fun u v -> u ^ (String.make 1 v)) "" ls
	let (@@@) = (@) let (@) a i = a.(~|i) let (<@) a (i,v) = a.(~|i) <- v
	let ceildiv m n = (m+n-1L) / n
end open MyInt64

let () =
	let n,x = get_2_i64 0 in
	let a = input_i64_array n
	in
	let a = Array.map (fun v -> labs (v - x)) a in
	Array.fold_left (fun u v ->
		gcd u v
	) a.(0) a
	|> printf "%Ld\n"