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 Common Lisp (SBCL 1.1.14) (judge verdict: Time Limit Exceeded)

(defun split (input stack-string output-list)
  (let ((chara (car input)))
    (case chara
          ((nil) (append output-list (list stack-string)))
          (#\space (split (cdr input)
                          '()
                          (append output-list (list stack-string))))
          (otherwise (split (cdr input)
                            (concatenate 'string stack-string (list chara))
                            output-list)))))

(defun input-to-list (input)
  (mapcar #'parse-integer (split (concatenate 'list input)
                                 '()
                                 '())))

(defvar kn (input-to-list (read-line)))
(defvar a (input-to-list (read-line)))

#| (defun submax (lst)
  (labels ((inner (lst candidate)
                  (if (cdr lst)
                      (let ((challenger (- (cadr lst) (car lst))))
                        (if (< candidate challenger)
                            (inner (cdr lst) challenger)
                            (inner (cdr lst) candidate)))
                      candidate)))
          (inner lst 0))) |#

(defun submax (lst)
  (labels ((inner (lst candidate)
                  (if (cdr lst)
                      (inner (cdr lst)
                             (let ((challenger (- (cadr lst) (car lst))))
                               (if (< candidate challenger)
                                   challenger
                                   candidate)))
                      candidate)))
          (inner lst 0)))

(princ (- (car kn) (submax (append a
                                   (list (+ (car kn) (car a)))))))