using System;
using System.Linq;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            ABC160.C();
        }
        class ABC160
        {
            public static void A()
            {
                var s = Read.Str();
                Console.WriteLine(s[2] == s[3] && s[4] == s[5] ? "Yes" : "No");
            }
            public static void B()
            {
                var X = Read.Long();
                Console.WriteLine(X / 500 * 1000 + (X % 500) / 5 * 5);
            }
            public static void C()
            {
                var K = Read.Long();
                var N = Read.Int();
                var A = Read.IntN();
                var max = K + A[0] - A[N - 1];
                for(int i = 0; i < N - 1; ++i)
                {
                    max = Math.Max(max, A[i + 1] - A[i]);
                }
                Console.WriteLine(K - max);
            }
            public static void D()
            {
                var N = Read.Int();
                var X = Read.Int();
                var Y = Read.Int();

            }
            public static void E()
            {
                var X = Read.Int();
                var Y = Read.Int();
                var A = Read.Int();
                var B = Read.Int();
                var C = Read.Int();
                var P = Read.LongN();
                var Q = Read.LongN();
                var R = Read.LongN();
                List<Tuple<long, int>> list = new List<Tuple<long, int>>();
                for(int i = 0; i < A; ++i)
                {
                    list.Add(new Tuple<long, int>(P[i], 0));
                }
                for (int i = 0; i < B; ++i)
                {
                    list.Add(new Tuple<long, int>(Q[i], 1));
                }
                for (int i = 0; i < C; ++i)
                {
                    list.Add(new Tuple<long, int>(R[i], 2));
                }
                list = list.OrderBy(x => -x.Item1).ToList();
                long sum = 0;
                int countX = 0;
                int countY = 0;
                int res = X + Y;
                int idx = 0;
                while (res > 0)
                {
                    var a = list[idx];
                    switch (a.Item2)
                    {
                        case 0:
                            if (countX < X)
                            {
                                sum += a.Item1;
                                countX++;
                                res--;
                            }
                            break;
                        case 1:
                            if (countY < Y)
                            {
                                sum += a.Item1;
                                countY++;
                                res--;
                            }
                            break;
                        case 2:
                            sum += a.Item1;
                            res--;
                            break;
                    }
                    idx++;
                }
                Console.WriteLine(sum);
            }
            public static void F()
            {

            }
        }
        class Util
        {
        }

        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(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 = Read.IntN();
                    dict[ab[0]].Add(ab[1]);
                    dict[ab[1]].Add(ab[0]);
                }
                return dict;
            }
            public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
            {
                Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new Dictionary<int, long>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1], ab[2]);
                    dict[ab[1]].Add(ab[0], ab[2]);
                }
                return dict;
            }
        }
    }
}


Measured memory_bytes: 35036