Problem:
Score : 300 points

Problem Statement

There is a circular pond with a perimeter of K meters, and N houses around them.

The i-th house is built at a distance of A_i meters from the northmost point of the pond, measured clockwise around the pond.

When traveling between these houses, you can only go around the pond.

Find the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Constraints

2 \leq K \leq 10^6

2 \leq N \leq 2 \times 10^5

0 \leq A_1 < ... < A_N < K

All values in input are integers.

Input

Input is given from Standard Input in the following format:

K N
A_1 A_2 ... A_N

Output

Print the minimum distance that needs to be traveled when you start at one of the houses and visit all the N houses.

Sample Input 1

20 3
5 10 15

Sample Output 1

10

If you start at the 1-st house and go to the 2-nd and 3-rd houses in this order, the total distance traveled will be 10.

Sample Input 2

20 3
0 5 15

Sample Output 2

10

If you start at the 2-nd house and go to the 1-st and 3-rd houses in this order, the total distance traveled will be 10.

Solution in OCaml (4.02.3) (judge verdict: Time Limit Exceeded)

(*
ocamlfind ocamlopt -package batteries -linkpkg main.ml -o a.out
*)
open Batteries

let k, n = Scanf.sscanf (read_line ()) "%d %d" (
        fun k n -> 
                k, n
)

let lst = Str.split (Str.regexp " ") (read_line ())
          |> List.map int_of_string 
          |> List.sort compare

let rec f head tail lst =
        match lst with
                  [] -> [0]
                | first :: [] -> 
                        [head + (k - tail)] @ f head tail []  
                | first :: rest -> 
                        [(List.hd rest) - first] @ f head tail rest

let () =
        let tmplst = f (List.min lst) (List.max lst) lst in
        let tmplst2 = List.filter (fun elmnt ->
                elmnt != (List.max tmplst)
        ) tmplst in
                List.fold_right (+) tmplst2 0
                |> Printf.printf "%d\n"