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: Wrong Answer)

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


    public class Program
    {
        public static void Main(string[] args)
        {
            new C().test();
        }
    }

	public class C
	{
		public void test()
		{
			// 整数の入力
			List<int> kn = CommonRead.ReadIntL();
			List<int> ai = CommonRead.ReadIntL();

			//周回した値
			var enn = kn[0];

			// 点の間が一番大きい数字を判定する
			for (var i = ai.Count() -1; i>0; i--)
			{

				//生回転
				var tmp1 = 0;
				if (i == ai.Count() - 1)
				{
					tmp1 = kn[0] - ai[i] + ai[0] ;
				}
				else
				{
					tmp1 = ai[i+1] - ai[i];
				}


				var tmp2 = 0;
				//逆回転
				if (i == 1)
				{
					tmp2 = kn[0] - ai[i] + ai[0];
				}
				else
				{
					tmp2 = ai[i] - ai[i - 1];
				}


				// 同一なら次の要素
				if (tmp1 == tmp2) continue;


				// どっち周りかわかる

				//逆回転
				if (tmp1 > tmp2)
				{
					enn = kn[0] - tmp1;
				}
				// 正回転
				else
				{
					enn = kn[0] - tmp2;
				}


			break;


			}

			//出力
			Console.WriteLine(enn);
		}
	}


static class CommonRead
{
    public static string ReadStr()
    {
        return Console.ReadLine();
    }
    public static string[] ReadStrA()
    {
        return ReadStr().Split(' ');
    }
    public static List<string> ReadStrL()
    {
        return ReadStrA().ToList();
    }
    public static int ReadInt()
    {
        return Convert.ToInt32(ReadStr());
    }
    public static int[] ReadIntA()
    {
        return ReadStrA().Select(s => Convert.ToInt32(s)).ToArray();
    }
    public static List<int> ReadIntL()
    {
        return ReadStrA().Select(s => Convert.ToInt32(s)).ToList();
    }
    public static long ReadLong()
    {
        return Convert.ToInt64(ReadStr());
    }
    public static long[] ReadLongA()
    {
        return ReadStrA().Select(s => Convert.ToInt64(s)).ToArray();
    }
    public static List<long> ReadLongL()
    {
        return ReadStrA().Select(s => Convert.ToInt64(s)).ToList();
    }

    public static decimal ReadDecimal()
    {
        return Convert.ToDecimal(ReadStr());
    }
    public static decimal[] ReadDecimalA()
    {
        return ReadStrA().Select(s => Convert.ToDecimal(s)).ToArray();
    }
    public static List<decimal> ReadDecimalL()
    {
        return ReadStrA().Select(s => Convert.ToDecimal(s)).ToList();
    }

    public static double ReadDouble()
    {
        return Convert.ToDouble(ReadStr());
    }
    public static double[] ReadDoubleA()
    {
        return ReadStrA().Select(s => Convert.ToDouble(s)).ToArray();
    }
    public static List<double> ReadDoubleL()
    {
        return ReadStrA().Select(s => Convert.ToDouble(s)).ToList();
    }

}