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: Accepted)

using System.Collections;
using System.Text;
using System.Threading.Tasks;
using static System.Math;
using static System.Console;
using System.Collections.Generic;
using System.Linq;
using System;
using System.Numerics;


class Program
{

    static void Main()
    {
        int[] KN = ReadInts;
        int K = KN[0];
        int N = KN[1];

        int[] As = ReadInts;

        int maxD = K-(As[N-1] - As[0]);

        for (int i = 1; i < N; i++)
        {
            maxD = Max(maxD,As[i] - As[i - 1]);
        }

        WriteLine(K-maxD);
        ReadLine();
    }


    struct Vector2Int
    {
        public Vector2Int(int x, int y)
        {
            X = x;
            Y = y;
        }
        public int X;
        public int Y;
        public double Magnitude => Math.Sqrt(X * X + Y * Y);

        public static Vector2Int zero => new Vector2Int(0, 0);
        public static Vector2Int u => new Vector2Int(0, 1);
        public static Vector2Int r => new Vector2Int(1, 0);
        public static Vector2Int d => new Vector2Int(0, -1);
        public static Vector2Int l => new Vector2Int(-1, 0);
        public static Vector2Int[] AllDirections => new Vector2Int[4] { u, r, d, l };
        public static Vector2Int[] AllDirections8 => new Vector2Int[8] { u, r, d, l, u + r, r + d, d + l, l + u };


        public static Vector2Int operator +(Vector2Int a, Vector2Int b)
        {
            return new Vector2Int(a.X + b.X, a.Y + b.Y);
        }
        public static Vector2Int operator -(Vector2Int a, Vector2Int b)
        {
            return new Vector2Int(a.X - b.X, a.Y - b.Y);
        }
        public static bool operator ==(Vector2Int a, Vector2Int b)
        {
            return a.X == b.X && a.Y == b.Y;
        }
        public static bool operator !=(Vector2Int a, Vector2Int b)
        {
            return a.X != b.X || a.Y != b.Y;
        }
        public static Vector2Int operator *(Vector2Int v, int n)
        {
            return new Vector2Int(v.X * n, v.Y * n);
        }
        public static Vector2Int operator *(int n, Vector2Int v)
        {
            return new Vector2Int(v.X * n, v.Y * n);
        }
    }
    struct Vector3Int
    {
        public Vector3Int(int x, int y, int z)
        {
            X = x;
            Y = y;
            Z = z;
        }
        public int X;
        public int Y;
        public int Z;

        public double Magnitude => Math.Sqrt(X * X + Y * Y + Z * Z);

        public static Vector3Int zero => new Vector3Int(0, 0, 0);
        public static Vector3Int u => new Vector3Int(0, 1, 0);
        public static Vector3Int r => new Vector3Int(1, 0, 0);
        public static Vector3Int d => new Vector3Int(0, -1, 0);
        public static Vector3Int l => new Vector3Int(-1, 0, 0);

        public static Vector3Int operator +(Vector3Int a, Vector3Int b)
        {
            return new Vector3Int(a.X + b.X, a.Y + b.Y, a.Z + b.Z);
        }
        public static Vector3Int operator -(Vector3Int a, Vector3Int b)
        {
            return new Vector3Int(a.X - b.X, a.Y - b.Y, a.Z - b.Z);
        }
        public static bool operator ==(Vector3Int a, Vector3Int b)
        {
            return a.X == b.X && a.Y == b.Y && a.Z == b.Z;
        }
        public static bool operator !=(Vector3Int a, Vector3Int b)
        {
            return a.X != b.X || a.Y != b.Y || a.Z != b.Z;
        }
        public static Vector3Int operator *(Vector3Int v, int n)
        {
            return new Vector3Int(v.X * n, v.Y * n, v.Z * n);
        }
        public static Vector3Int operator *(int n, Vector3Int v)
        {
            return new Vector3Int(v.X * n, v.Y * n, v.Z * n);
        }
    }

    #region Reader
    static Vector2Int ReadVec2Int
    {
        get
        {
            string[] s = Console.ReadLine().Split(' ');
            return new Vector2Int(int.Parse(s[0]), int.Parse(s[1]));
        }
    }
    static Vector2Int[] ReadVec2Ints(int n)
    {
        List<Vector2Int> list = new List<Vector2Int>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadInts;
            list.Add(new Vector2Int(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static HashSet<Vector2Int> ReadVec2IntHash(int n)
    {
        HashSet<Vector2Int> hash = new HashSet<Vector2Int>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadInts;
            hash.Add(new Vector2Int(ab[0], ab[1]));
        }
        return hash;
    }
    static string ReadStr => Console.ReadLine();
    static string[] ReadStrs => Console.ReadLine().Split(' ');
    static int ReadInt => Convert.ToInt32(Console.ReadLine());
    static int[] ReadInts => Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray();
    static long ReLong => Convert.ToInt64(Console.ReadLine());
    static long[] ReadLongs => Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray();
    static long[,] ReLongMatrix(int r, int c)
    {
        var mat = new long[r, c];
        for (int i = 0; i < r; ++i)
        {
            var x = ReadLongs;
            for (int j = 0; j < c; ++j)
            {
                mat[i, j] = x[j];
            }
        }
        return mat;
    }
    static Tuple<string, string>[] ReTupleStr(int n)
    {
        List<Tuple<string, string>> list = new List<Tuple<string, string>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadStrs;
            list.Add(new Tuple<string, string>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Tuple<long, long>[] ReTupleLong(int n)
    {
        List<Tuple<long, long>> list = new List<Tuple<long, long>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadLongs;
            list.Add(new Tuple<long, long>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Tuple<int, int>[] ReadTupleInt(int n)
    {
        List<Tuple<int, int>> list = new List<Tuple<int, int>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadInts;
            list.Add(new Tuple<int, int>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Tuple<double, double>[] ReTupleDouble(int n)
    {
        List<Tuple<double, double>> list = new List<Tuple<double, double>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadLongs;
            list.Add(new Tuple<double, double>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Dictionary<int, HashSet<int>> ReAdjacencyList(int N, int M)
    {
        Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
        for (int i = 0; i <= N; ++i)
        {
            dict.Add(i, new HashSet<int>());
        }
        for (int i = 0; i < M; ++i)
        {
            var ab = ReadInts;
            dict[ab[0]].Add(ab[1]);
            dict[ab[1]].Add(ab[0]);
        }
        return dict;
    }
    #endregion
}