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;
using System.Linq;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using static System.Console;
using static Program.Input;
using static Program.MyMath;
using static Program.Const;

namespace Program
{
    static class Const
    {
        public static string alp = "abcdefghijklmnopqrstuvwxyz";
        public static string Alp = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
        public const long MOD = 1000000007;
        public static int INF = int.MaxValue;
        public static long INFL = long.MaxValue;
    }
    public static class Program
    {
        public static void Main()
        {
            long k, n;
            InputLine(out k, out n);
            var a = ScanLongArray();
            var b = new long[n];
            b[0] = a[0] + k - a[n - 1];
            for(int i=1; i<n; i++)
            {
                b[i] = a[i] - a[i - 1];
            }
            WriteLine(b.Sum() - b.Max());
            //ReadKey();
        }
    }
    static class Input
    {
        public static void InputLine(out int a, out int b) { var input = ScanIntArray(); a = input[0]; b = input[1]; }
        public static void InputLine(out int a, out int b, out int c) { var input = ScanIntArray(); a = input[0]; b = input[1]; c = input[2]; }
        public static void InputLine(out int a, out int b, out int c, out int d) { var input = ScanIntArray(); a = input[0]; b = input[1]; c = input[2]; d = input[3]; }

        public static void InputLine(out long a, out long b) { var input = ScanLongArray(); a = input[0]; b = input[1]; }
        public static void InputLine(out long a, out long b, out long c) { var input = ScanLongArray(); a = input[0]; b = input[1]; c = input[2]; }
        public static void InputLine(out long a, out long b, out long c, out long d) { var input = ScanLongArray(); a = input[0]; b = input[1]; c = input[2]; d = input[3]; }

        public static void InputLine(out string a, out string b) { var input = ScanStrArray(); a = input[0]; b = input[1]; }

        public static int ScanInt() { return int.Parse(ReadLine()); }
        static public uint ScanUint() { return uint.Parse(ReadLine()); }
        static public double ScanDouble() { return double.Parse(ReadLine()); }
        static public long ScanLong() { return long.Parse(ReadLine()); }
        static public ulong ScanUlong() { return ulong.Parse(ReadLine()); }
        static public int[] ScanIntArray() { return ReadLine().Split().Select(x => int.Parse(x)).ToArray(); }
        static public uint[] ScanUintArray() { return ReadLine().Split().Select(x => uint.Parse(x)).ToArray(); }
        static public double[] ScanDoubleArray() { return ReadLine().Split().Select(x => double.Parse(x)).ToArray(); }
        static public long[] ScanLongArray() { return ReadLine().Split().Select(x => long.Parse(x)).ToArray(); }
        static public ulong[] ScanUlongArray() { return ReadLine().Split().Select(x => ulong.Parse(x)).ToArray(); }

        static public string ScanStr() { return ReadLine(); }
        static public string[] ScanStrArray() { return ScanStr().Split(); }
        static public string RegaxReplace(this string arg1, string pattern, string replacement) { return Regex.Replace(arg1, pattern, replacement); }
    }
    static class MyMath
    {
        static public int CountBit(this long a) { if (a == 0) return 0; int c = 1; for (; a > 1; a /= 2) if (a % 2 == 1) c++; return c; }
        static public int Floor2(this int a) { int N = 1; while (N < a) N *= 2; return N / 2; }
        static public long Floor2(this long a) { long N = 1; while (N < a) N *= 2; return N / 2; }
        static public int Ceiling2(this int a) { int N = 1; while (N < a) N *= 2; return N; }
        static public long Ceiling2(this long a) { long N = 1; while (N < a) N *= 2; return N; }
        static public long[] CumSum(this long[] a) { var res = new long[a.Length]; long s = 0; for (int i = 0; i < a.Length; i++) res[i] = (s += a[i]); return res; }
        static public IEnumerable<int> PrimeFactors(this int n)
        {
            int tmp = n;
            for (int i = 2; i * i <= n; i++) while (tmp % i == 0) { tmp /= i; yield return i; }
            if (tmp != 1) yield return tmp;
        }
        static public IEnumerable<long> PrimeFactors(this long n)
        {
            var tmp = n;
            for (long i = 2; i * i <= n; i++) while (tmp % i == 0) { tmp /= i; yield return i; }
            if (tmp != 1) yield return tmp;
        }
        static public int Digit(this int n, int d) { if (d < 0) return 0; return (n % (int)Math.Pow(10, d + 1)) / (int)Math.Pow(10, d); }
        static public int Length(this int n) { if (n < 0) return 0; return (int)Math.Log10(n) + 1; }
        static public int Top(this int n) { return n.Digit(n.Length() - 1); }
        public static bool isPrime(this int p)
        {
            if (p <= 1) return false;
            for (int i = 2; i * i <= p; i++) if (p % i == 0) return false;
            return true;
        }
        public static bool isPrime(this long p)
        {
            if (p <= 1) return false;
            for (long i = 2; i * i <= p; i++) if (p % i == 0) return false;
            return true;
        }
        public static int GCD(int a, int b)
        {
            Func<int, int, int> gcd = null;
            gcd = (x, y) => y == 0 ? x : gcd(y, x % y);
            return a > b ? gcd(a, b) : gcd(b, a);
        }
        public static long GCD(long a, long b)
        {
            Func<long, long, long> gcd = null;
            gcd = (x, y) => y == 0 ? x : gcd(y, x % y);
            return a > b ? gcd(a, b) : gcd(b, a);
        }
        public static ulong extGCD(ulong a, ulong b, ref ulong x, ref ulong y)
        {
            if (b == 0) { x = 1; y = 0; return a; }
            var d = extGCD(b, a % b, ref y, ref x);
            y -= a / b * x;
            return d;
        }
        public static int LCM(int a, int b) { return a * b / GCD(a, b); }
        public static long LCM(long a, long b) { return a * b / GCD(a, b); }
        public static long Inv(this long a, long m = MOD)
        {
            long b = m, u = 1, v = 0;
            while (b != 0)
            {
                long t = a / b;
                a -= t * b;
                swap(ref a, ref b);
                u -= t * v;
                swap(ref u, ref v);
            }
            u %= m;
            if (u < 0) u += m;
            return u;
        }
        private static void swap(ref long a, ref long b) { var t = a; a = b; b = t; }
        public static long ModPow(long a, long n, long m = MOD)
        {
            long res = 1;
            while (n > 0)
            {
                if (n % 2 == 1) res = (res * a) % m;
                a = (a * a) % m;
                n >>= 1;
            }
            return res;
        }
    }

    static class MyLinq
    {
        public static void Sort(this string[] array) { Array.Sort(array, StringComparer.OrdinalIgnoreCase); }
        public static void StringSort(this List<string> list) { list.Sort(StringComparer.OrdinalIgnoreCase); }
        public static string Join<T>(this IEnumerable<T> source, string separator) { return string.Join(separator, source); }
        public static IEnumerable<TItem> Distinct<TItem, TKey>(this IEnumerable<TItem> source, Func<TItem, TKey> keySelector)
        {
            if (source == null)
                throw new ArgumentNullException(nameof(source));

            if (keySelector == null)
                throw new ArgumentNullException(nameof(keySelector));

            var set = new HashSet<TKey>();
            foreach (var item in source)
                if (set.Add(keySelector(item))) yield return item;
        }
    }
}