Problem:
Score : 700 points

Problem Statement

Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).

Now, he will perform the following operation exactly once:

Choose K consecutive elements in P and sort them in ascending order.

Find the number of permutations that can be produced as P after the operation.

Constraints

2 \leq N \leq 200000

2 \leq K \leq N

0 \leq P_i \leq N-1

P_0,P_1,\cdots,P_{N-1} are all different.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
P_0 P_1 \cdots P_{N-1}

Output

Print the number of permutations that can be produced as P after the operation.

Sample Input 1

5 3
0 2 1 4 3

Sample Output 1

2

Two permutations can be produced as P after the operation: (0,1,2,4,3) and (0,2,1,3,4).

Sample Input 2

4 4
0 1 2 3

Sample Output 2

1

Sample Input 3

10 4
2 0 1 3 7 5 4 6 8 9

Sample Output 3

6

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

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

namespace A
{
    class StartingPoint
    {
        static void Main(string[] args)
        {
            if (args?.Any() == true)
            {
                var assembly = Assembly.GetEntryAssembly();
                var resourceName = "AtCoderCSharp.In.txt";
                var stream = assembly.GetManifestResourceStream(resourceName);
                var streamReader = new StreamReader(stream, Encoding.UTF8);
                var str = streamReader.ReadToEnd();
                var textReader = new StringReader(str);
                Console.SetIn(textReader);
            }

            try
            {
                foreach (var s in new Program().Solve())
                {
                    Console.WriteLine(s);
                }
            }
            catch (Exception e)
            {
                Console.WriteLine(e);
                if (args?.Any() != true)
                    throw e;
            }

            if (args?.Any() == true)
                Console.ReadKey();
        }
    }

    class Program
    {
        public List<int> ScanInts(int count) => Enumerable.Range(0, count).Select(_ => ScanInt).ToList();
        public List<int> ScanInts(long count) => ScanInts((int)count);
        public List<long> ScanLongs(int count) => Enumerable.Range(0, count).Select(_ => Scan).ToList();
        public List<long> ScanLongs(long count) => ScanLongs((int)count);
        public int ScanInt => int.Parse(Str);
        public long Scan => long.Parse(Str);
        public double ScanDouble => (double)Scan;

        StringBuilder sb = new StringBuilder();

        public string Str => ScanStr();
        public string ScanStr()
        {
            sb.Clear();

            int r = 0;
            bool? b = null;
            do
            {
                r = Console.Read();
                b = IsBreak(r);
            } while (b == true);

            if (b == null)
                throw new Exception("input error: unexpected end of stream");

            do
            {
                sb.Append((char)r);
                r = Console.Read();
                b = IsBreak(r);
            } while (b == false);

            return sb.ToString();
        }

        bool? IsBreak(int c)
        {
            switch (c)
            {
                case -1:
                    return null;
                case (int)' ':
                case (int)'\n':
                case (int)'\r':
                    return true;
                default:
                    return false;
            }
        }

        public IEnumerable<int> Loop(int count) => Enumerable.Range(0, count);
        public IEnumerable<int> Loop(int from, int to) => Enumerable.Range(from, to - from + 1);

        public IEnumerable<long> Loop(long count) => Loop(0, count - 1);
        public IEnumerable<long> Loop(long from, long to)
        {
            for (long i = from; i <= to; i++)
                yield return i;
        }

        public string YesNo(bool isYes) => isYes ? "Yes" : "No";

        public HashSet<T> ToHashSet<T>(IEnumerable<T> ts) => new HashSet<T>(ts);

        HashSet<int> GetNonOrder(List<int> p, int k)
        {
            var result = new HashSet<int>();
            var po = 0;

            for (int i = 1; i < p.Count; i++)
            {
                if (p[i - 1] > p[i])
                    po = i;

                if (po + k - 1 <= i)
                    result.Add(i);
            }

            return result;
        }

        public IEnumerable<string> Solve()
        {
            var n = ScanInt;
            var k = ScanInt;
            var p = ScanInts(n);

            //var r = new Random();
            //n = 200000;
            //p = Enumerable.Range(0, n).OrderBy(_ => r.Next()).ToList();


            var nonOrder = GetNonOrder(p, k);
            var res = nonOrder.Any() ? 1 : 0;

            var sortedSet = new SortedSet<int>();

            for (int i = 0; i < k; i++)
            {
                sortedSet.Add(p[i]);
            }
            if (nonOrder.Contains(k - 1) == false)
                res++;

            for (int i = k; i < n; i++)
            {
                var first = sortedSet.First();
                var last = sortedSet.Last();
                bool b = (first != p[i - k] || last > p[i]) && nonOrder.Contains(i) == false;
                if (b)
                    res++;

                sortedSet.Remove(p[i - k]);
                sortedSet.Add(p[i]);
            }

            yield return res.ToString();
        }
    }
}