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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.Scanner;


public class Main {

    static void solve() {
        Scanner scan = new Scanner(System.in);
        int k = scan.nextInt();
        int n = scan.nextInt();
        int[] arr = new int[n];
        for(int i=0;i<n;i++) {
            arr[i] = scan.nextInt();
        }
        //arr[n] = arr[0];
        //long min = Long.MAX_VALUE;
        Arrays.sort(arr);
        int sum = 0;
        int maxDiff = 0;
        for(int i=1;i<n;i++) {
            int diff = arr[i]-arr[i-1];
            maxDiff = Math.max(maxDiff, diff);
            sum += diff;

        }
        int finalDiff = k-arr[n-1]+arr[0];
        maxDiff = Math.max(maxDiff, finalDiff);
        sum+=k-arr[n-1] + arr[0];

        int res = sum - maxDiff;
        System.out.println(res);
    }


    public static void main(String[] args) {

        solve();

        //        Main m = new Main();
        //        Scanner scan = new Scanner(System.in);

        //        long n = scan.nextLong();
        //        long r = scan.nextLong();
        //        List<Long> list = new ArrayList<>();
        ////        int[] arr = new int[n];
        //        for (long i=0;i<n;i++){
        //            list.add(scan.nextLong());
        //        }
//            System.out.println(ch);
        //        solve(n, arr);
        //        scan.close();
    }


    class Counter extends HashMap<Integer, Integer> {
        public int get(int k) {
            return containsKey(k) ? super.get(k) : 0;
        }

        public void add(int k, int v) {
            put(k, get(k) + v);
        }
    }



    static class Node {
        int val;
        Node next;
        Node random;

        public Node(int val) {
            this.val = val;
            this.next = null;
            this.random = null;
        }
    }

//    static class Node {
//        int key;
//        int data;
//        Node next;
//        Node prev;
//
//        Node(int key, int data) {
//            this.key = key;
//            this.data = data;
//        }
//    }

    static class TreeNode {
        int val;
        TreeNode left;
        TreeNode right;

        TreeNode(int x) {
            val = x;
        }
    }

    static class Trie {
        void add(String word) {

        }

        boolean search(String w) {
            return false;
        }
    }

    static class Node1 {
        public int val;
        public List<Node1> children;

        public Node1() {
        }

        public Node1(int _val, List<Node1> _children) {
            val = _val;
            children = _children;
        }
    }

    ;

    static class TrieNode {

    }

    static class KvNode implements Comparable<KvNode> {
        String key;
        int freq;

        public KvNode(String key, int freq) {
            this.key = key;
            this.freq = freq;
        }

        @Override
        public int compareTo(KvNode o) {
            if (this.key.equals(o.key)) {
                return 0;
            }
            return Integer.compare(o.freq, this.freq);
        }
    }

    static class ListNode {
        int val;
        ListNode next;

        ListNode(int x) {
            val = x;
        }
    }
}