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.Linq;

namespace agc038_b
{
    class Program
    {
        static void Main(string[] args)
        {
            List<int> input = Console.ReadLine().Split(' ').Select(int.Parse).ToList();
            int n = input[0];
            int k = input[1];

            List<int> pList = Console.ReadLine().Split(' ').Select(int.Parse).ToList();
            HashSet<string> result = new HashSet<string>();

            string beforeSort = "";

            int num = n - k + 1;

            for (int index = 0; index < num; index++)
            {
                List<int> sortList = new List<int>(pList.GetRange(index, k).OrderBy(x => x).ToList());
                if (index != 0)
                {
                    beforeSort += sortList.Last().ToString();
                    string thisSort = pList[index - 1].ToString() + string.Join("", sortList);
                    // before check
                    if (thisSort == beforeSort)
                    {
                        continue;
                    }
                }


                List<int> list = new List<int>(pList);
                string aaa = string.Join("", list);

                string ee = aaa.Substring(0, index) + string.Join("", sortList) + aaa.Substring(index + k);

                //for (int indexs = 0; indexs < k; indexs++)
                //{
                //    list[index + indexs] = sortList[indexs];
                //}


                //string ee = string.Join("", list);

                if (!result.Contains(ee))
                {
                    result.Add(ee);

                }

                beforeSort = string.Join("", sortList);
            }

            Console.WriteLine(result.Count);
        }
    }
}