using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.IO;
using System.Diagnostics;

class Myon
{
    public Myon() { }
    public static int Main()
    {
        new Myon().calc();
        return 0;
    }
    Scanner cin;
    Func cin2;
    public static long mod = 1000000007;
    void calc()
    {
        cin = new Scanner();
        cin2 = new Func();
        int K = cin.nextInt();
        int N = cin.nextInt();
        int[] a = cin.ArrayInt(N,0);
        Array.Sort(a);
        int ans=0;
        for(int i=1;i<N;i++)
        {
            ans=Math.Max(ans,a[i]-a[i-1]);
        }
        ans=Math.Max(ans,(K-a[N-1]+a[0]));
        Console.WriteLine(K-ans);
    }
}



class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }

    public int nextInt()
    {
        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextInt() + add;
        }
        return Array;
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextLong() + add;
        }
        return Array;
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextDouble() + add;
        }
        return Array;
    }
}

class Answer
{
    public void Int2DArrayAns(int[,]x,char c)
    {
        for(int i=0;i<x.GetLength(0);i++)
        {
            for(int j=0;j<x.GetLength(1)-1;j++)
            {
                Console.Write(x[i,j]);
                Console.Write(c);
            }
            Console.WriteLine(x[i,x.GetLength(1)-1]);
        }
    }
    public void Char2DArrayAns(char[,]x,char c)
    {
        for(int i=0;i<x.GetLength(0);i++)
        {
            for(int j=0;j<x.GetLength(1)-1;j++)
            {
                Console.Write(x[i,j]);
                Console.Write(c);
            }
            Console.WriteLine(x[i,x.GetLength(1)-1]);
        }
    }
}

class Func
{
    public static long mod = 1000000007;
    public long GCDLong(long a, long b)
    {
        while(a!=0)
        {
          long t=a;
          a=b%a;
          b= t;
        }
      
        return b;        
    }
    public long mod_pow(long x, long n)
    { 
        long ans = 1;
        while(n > 0)
        {
            if ((n & 1) == 1)
            {
                ans = ans * x;
                ans%=mod;
            }
            x = x*x%mod;
            n >>= 1;
        }
        return ans;
    }
    public long factorial(long x)
    {
        long n=1;
        if(x<=1) return x;
        else
        {
            n *= (x*factorial(x-1));
            n%=mod;
            return n;
        }
    }
    public long combination(long n, long r)
    {
        if ( r * 2 > n ) r = n - r;
		long dividend = 1;
		long divisor = 1;
		for ( long i = 1; i <= r; ++i ) {
			dividend *= ( n - i + 1 );
			dividend %= mod;
 
			divisor *= i;
			divisor %= mod;
		}
 
		return (dividend * mod_pow(divisor,mod - 2)) % mod;   
    }
}




Measured memory_bytes: 31708