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.Collections.Generic;

namespace AtCoder
{
	class Program
	{
		public static void Main()
		{
			var intArray = IO.ReadIntArray();
			var lakeDistance  =intArray[0];
			var buildNum = intArray[1];

			var positions = IO.ReadIntArray().ToList();
			positions.Insert(0 , positions[buildNum - 1] - lakeDistance);
			var maxDistance = 0;
			for(var iIndex = 1 ; iIndex <= buildNum ; ++ iIndex)
			{
				maxDistance = Math.Max(maxDistance , positions[iIndex] - positions[iIndex - 1]);
			}			
			IO.Write(lakeDistance - maxDistance);
		}
	}

	public static class IO
	{
		public static string   Read()							   { return Console.ReadLine(); }
		public static string[] ReadArray(char iSplitter = ' ')	   { return Read().Split(iSplitter); }
		public static int	   ReadInt()						   { return int.Parse(Read()); }
		public static int[]	   ReadIntArray(char iSplitter = ' ')  { return ReadArray().Select(iText => int.Parse(iText)).ToArray(); }
		public static long	   ReadLong()						   { return int.Parse(Read()); }
		public static long[]   ReadLongArray(char iSplitter = ' ') { return ReadArray().Select(iText => long.Parse(iText)).ToArray(); }
		public static char[]   ReadCharArray()					   { return Read().ToCharArray(); }

		public static void Write(string iValue)			  { Console.WriteLine(iValue); }
		public static void Write(int iValue)			  { Console.WriteLine(iValue); }
		public static void Write(IEnumerable<int> iValue) { Console.WriteLine(string.Join(" " , iValue)); }
		public static void Write(long iValue)			  { Console.WriteLine(iValue); }
		public static void Write(decimal iValue)		  { Console.WriteLine(iValue); }
		public static void Write(bool iValue)			  { Console.WriteLine(iValue ? "Yes" : "No"); }
	}

	public static class Util
	{
		public static long Gcd(long i0 , long i1) { return (i0 > i1) ? _Gcd(i0 , i1) : _Gcd(i1 , i0); }
		public static long Lcm(long i0 , long i1) { return (i0 * i1) / Gcd(i0 , i1); }
		public static long ModPow(long iBaseNumber , long iPow , long iModNumber)
		{
			var num = 1L;
			while(iPow != 0)
			{
				if((iPow & 0x1) != 0)
				{
					num = (num * iBaseNumber) % iModNumber;
				}
				iBaseNumber = (iBaseNumber * iBaseNumber) % iModNumber;
				iPow >>= 1;
			}
			return num;
		}

		private static long _Gcd(long i0 , long i1)	{ return (i1 == 0) ? i0 : _Gcd(i1 , i0 % i1); }
	}
}