using System;
using System.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Math;
using static System.Console;
using static exMath;
using static exReadLine;


class Program
{
    static void Main(string[] args)
    {
        long K, N;
        longReadLine(out K, out N);
        long[] A = longArrayReadLine();
        long ans = K;
        for (int i = 0; i < N; i++)
        {
            long L = 0;
            long R = 0;
            if(i == 0)
            {
                L = A[0] + (K - A[1]);
                R = A[N - 1] - A[0];
            }
            else if(i == N - 1)
            {
                L = A[i] - A[0];
                R = (K - A[N - 1]) + A[N - 2];
            }
            else
            {
                L = A[i] + (K - A[i + 1]);
                R = (K - A[i]) + A[i - 1];
            }

            if(L < ans || R < ans)
            {
                ans = Min(L, R);
            }
        }
        WriteLine(ans);
    }
}

static class exReadLine
{
    public static void intReadLine(out int a)
    {
        a = int.Parse(ReadLine());
    }
    public static void intReadLine(out int a, out int b)
    {
        int[] input = ReadLine().Split().Select(int.Parse).ToArray();
        a = input[0];
        b = input[1];
    }
    public static void intReadLine(out int a, out int b, out int c)
    {
        int[] input = ReadLine().Split().Select(int.Parse).ToArray();
        a = input[0];
        b = input[1];
        c = input[2];
    }
    public static void intReadLine(out int a, out int b, out int c, out int d)
    {
        int[] input = ReadLine().Split().Select(int.Parse).ToArray();
        a = input[0];
        b = input[1];
        c = input[2];
        d = input[3];
    }

    public static void longReadLine(out long a)
    {
        a = long.Parse(ReadLine());
    }
    public static void longReadLine(out long a, out long b)
    {
        long[] input = ReadLine().Split().Select(long.Parse).ToArray();
        a = input[0];
        b = input[1];
    }
    public static void longReadLine(out long a, out long b, out long c)
    {
        long[] input = ReadLine().Split().Select(long.Parse).ToArray();
        a = input[0];
        b = input[1];
        c = input[2];
    }
    public static void longReadLine(out long a, out long b, out long c, out long d)
    {
        long[] input = ReadLine().Split().Select(long.Parse).ToArray();
        a = input[0];
        b = input[1];
        c = input[2];
        d = input[3];
    }
    
    public static int[] intArrayReadLine()
    {
        return ReadLine().Split().Select(int.Parse).ToArray();
    }

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

    public static List<int> intListReadLine()
    {
        return ReadLine().Split().Select(int.Parse).ToList();
    }

    public static List<long> longListReadLine()
    {
        return ReadLine().Split().Select(long.Parse).ToList();
    }
}

static class exMath
{
    // 最大公約数
    public static int Gcd(int a, int b)
    {
        if (a < b) return Gcd(b, a);
        while (b != 0)
        {
            var r = a % b;
            a = b;
            b = r;
        }
        return a;
    }
    public static long Gcd(long a, long b)
    {
        if (a < b) return Gcd(b, a);
        while (b != 0)
        {
            var r = a % b;
            a = b;
            b = r;
        }
        return a;
    }

    // 最小公倍数
    public static long Lcm(int a, int b)
    {
        return BigMul(a, b) / Gcd(a, b);
    }
    public static long Lcm(long a, long b)
    {
        return a * b / Gcd(a, b);
    }
}

Measured memory_bytes: 36444