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

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            input_iter = LazyLoadAllLines();
            //------------------------------------------------//
            //var n = Read<long>();
            //var s = Read();
            //var als = Read<long>(n);
            //var sls = Read(n);
            //List<List<long>> abls = new List<List<long>>();
            //List<long> cls = new List<long>();
            /*List<long> edgeNum = Enumerable.Repeat(0L, (int)n).ToList();
            for (int i = 0; i < n - 1; ++i)
            {
                abls.Add(Read<long>(2));
                abls[i].Add(i);
                abls[i].Add(-1);
                --abls[i][0];
                --abls[i][1];
                //cls.Add(Read<long>());
                ++edgeNum[(int)abls[i][0]];
                ++edgeNum[(int)abls[i][1]];
            }*/

            //als.Sort((l, r) => (r - l));
            //sls.Sort(StringComparer.OrdinalIgnoreCase);

            // DP?Graph?
            // int -> long

            var k = Read<long>();
            var n = Read<long>();
            var als = Read<long>(n);

            List<long> betweenLen = new List<long>();

            betweenLen.Add(k - als[(int)n - 1] + als[0]);
            for (int i = 1; i < n; i++)
            {
                betweenLen.Add(als[i] - als[i - 1]);
            }

            Console.WriteLine(k - betweenLen.Max());
        }

        static IEnumerator<string> input_iter;

        static IEnumerator<string> LazyLoadAllLines(bool doSplit = true)
        {
            string line;
            if (doSplit)
            {
                do
                {
                    line = Console.ReadLine();
                    foreach (var s in line.Split(' '))
                        yield return s;
                } while (line != null);
            }
            else
            {
                do
                {
                    line = Console.ReadLine();
                    yield return line;
                } while (line != null);
            }
        }
        // single 1 elem.
        static _T Read<_T>() where _T : struct
        {
            input_iter.MoveNext();
            return (_T)Convert.ChangeType(input_iter.Current, typeof(_T));
        }
        static string Read()
        {
            input_iter.MoveNext();
            return input_iter.Current;
        }
        // single n-elems.
        static List<_T> Read<_T>(long num) where _T : struct
        {
            List<_T> res = new List<_T>();
            for (long i = 0; i < num; ++i)
            {
                input_iter.MoveNext();
                res.Add((_T)Convert.ChangeType(input_iter.Current, typeof(_T)));
            }
            return res;
        }
        static List<string> Read(long num)
        {
            List<string> res = new List<string>();
            for (long i = 0; i < num; ++i)
            {
                input_iter.MoveNext();
                res.Add(input_iter.Current);
            }
            return res;
        }
        // multiple(single type) n-elems. (Range, Edge etc.)
        static List<List<_T>> Read<_T>(long elemNum, long typeNum, bool toSort = false) where _T : struct
        {
            List<List<_T>> res = new List<List<_T>>();
            for (int i = 0; i < elemNum; ++i)
            {
                var elem = Read<_T>(typeNum);
                if (toSort) elem.Sort();
                res.Add(elem);
            }
            return res;
        }
        // multiple(multiple type) n-elems.
        static List<Tuple<_T1, _T2>> Read<_T1, _T2>(long num) where _T1 : struct where _T2 : struct
        {
            List<Tuple<_T1, _T2>> res = new List<Tuple<_T1, _T2>>();
            for (int i = 0; i < num; ++i)
            {
                res.Add(Tuple.Create(Read<_T1>(), Read<_T2>()));
            }
            return res;
        }
    }
}


Measured memory_bytes: 39136