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.Linq;
class Program
{
  static void Main (string[] args)
  {
    string[] input = Console.ReadLine().Split(' ');
    int N = int.Parse(input[0]);
    int K = int.Parse(input[1]);
    input = Console.ReadLine().Split(' ');
    int[] array = new int[N];
    for (int i = 0; i < N; i++) {
      array[i] = int.Parse(input[i]);
    }
    
    int sortCount = N - K + 1;
    string[] strs = new string[sortCount];
    for (int i = 0; i < sortCount; i++) {
      // 要素のソート
      int[] sortArray = new int[K];
      for (int j = 0; j < K; j++) {
        sortArray[j] = array[i+j];
      }
      Array.Sort(sortArray);
      
      // ソート部分より前を結合
      string s = string.Empty;
      for (int j = 0; j < i; j++) {
        s += array[j];
      }
      // ソート部分を結合
      for (int j = 0; j < K; j++) {
        s += sortArray[j];
      }
      // ソート部分より後を結合
      for (int j = (i + K); j < N; j++) {
        s += array[j];
      }
      strs[i] = s;
    }
    Console.WriteLine(strs.Distinct().ToArray().Length);
  }
}