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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Numerics;
using System.Collections;
namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var inp = Inputer.IntArray1Line();
            var K = inp[0];
            var N = inp[1];

            var A = Inputer.IntArray1Line();
            var p = Permutation<int>.All(A);

            var min = 2000000;
            foreach(int[] i in p)
            {

                var sum = 0;
                
                for(int j = 0; j < i.Length - 1; j++)
                {
                    if(Math.Abs(i[j]-i[j+1]) > K / 2)
                    {
                        sum += Math.Abs(Math.Max(i[j], i[j + 1])-K - Math.Min(i[j], i[j + 1]));
                    }
                    else
                    {
                        sum += Math.Abs(i[j] - i[j + 1]);
                    }
                }
                if (sum < min) min = sum;
            }
            Console.WriteLine(min);


        }






    }


    /// <summary>
    /// 素数かどうか判定する
    /// </summary>
    static class IsPrime
    {
        /// <summary>
        /// 素数かどうか判定
        /// </summary>
        /// <param name="num"></param>
        /// <returns></returns>
        public static bool Is(int num)
        {
            if (num < 2) return false;
            else if (num == 2) return true;
            else if (num % 2 == 0) return false;

            double sqrtNum = Math.Sqrt(num);
            for (int i = 3; i <= sqrtNum; i += 2)
            {
                if (num % i == 0)
                {

                    return false;
                }
            }


            return true;
        }

    }

    /// <summary>
    /// 入力受付
    /// </summary>
    static class Inputer
    {
        /// <summary>
        /// A B C の複数整数からなる1行を受け取る
        /// </summary>
        /// <returns></returns>
        public static int[] IntArray1Line()
        {
            return Console.ReadLine().Split().Select(int.Parse).ToArray();
        }
        /// <summary>
        /// A B C の複数整数からなる1行を受け取る
        /// </summary>
        /// <returns></returns>
        public static double[] DoubleArray1Line()
        {
            return Console.ReadLine().Split().Select(double.Parse).ToArray();
        }

        /// <summary>
        /// 整数N　のような１つの整数からなる入力を受け取る
        /// </summary>
        /// <returns></returns>
        public static int Int1Char()
        {
            return int.Parse(Console.ReadLine());
        }
        public static double Double1Char()
        {
            return double.Parse(Console.ReadLine());
        }

        /// <summary>
        /// 大きい整数N　のような１つの整数からなる入力を受け取る
        /// </summary>
        /// <returns></returns>
        public static long Long1Char()
        {
            return long.Parse(Console.ReadLine());

        }

        public static List<int> MultLineInt(int Linenum)
        {
            var L = new List<int>();
            for (int i = 0; i < Linenum; i++)
            {
                L.Add(int.Parse(Console.ReadLine()));
            }
            return L;
        }

        public static long[] LongArray1Line()
        {
            return Console.ReadLine().Split().Select(long.Parse).ToArray();
        }

        public static Char[] CharArray()
        {
            return Console.ReadLine().ToCharArray();
        }

    }

    /// <summary>
    /// 順列を出すやつ
    /// </summary>
    /// <typeparam name="T"></typeparam>
    static class Permutation<T>
    {
        private static void Search(List<T[]> perms, Stack<T> stack, T[] a)
        {
            int N = a.Length;
            if (N == 0)
            {
                perms.Add(stack.Reverse().ToArray());
            }
            else
            {
                var b = new T[N - 1];
                Array.Copy(a, 1, b, 0, N - 1);
                for (int i = 0; i < a.Length; ++i)
                {
                    stack.Push(a[i]);
                    Search(perms, stack, b);
                    if (i < b.Length) { b[i] = a[i]; }
                    stack.Pop();
                }
            }
        }
        public static IEnumerable<T[]> All(IEnumerable<T> src)
        {
            var perms = new List<T[]>();
            Search(perms, new Stack<T>(), src.ToArray());
            return perms;
        }
    }

    /// <summary>
    /// 素因数分解
    /// </summary>
    static class PrimeFactors
    {
        public static IEnumerable<long> PrimeFactor(long n)
        {
            long i = 2;
            long tmp = n;

            while (i * i <= n)
            {
                if (tmp % i == 0)
                {
                    tmp /= i;
                    yield return i;
                }
                else
                {
                    i++;
                }
            }
            if (tmp != 1) yield return tmp;//最後の素数も返す
        }

    }

}