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: Wrong Answer)

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

namespace B
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var nk = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
            var n = nk[0];
            var k = nk[1];
            var pi = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
            var answer = n - k + 1;
            for (var i = 0; i < pi.Length - k; i++)
            {
                var max = 0;
                var min = 1000000000;
                var prev = pi[i];
                for (var j = i; j < i + k; j++)
                {
                    max = Math.Max(max, pi[j]);
                    min = Math.Min(min, pi[j]);
                    prev = pi[j];
                }
                if (min > (i > 0 ? pi[i] : -1) && max < pi[i + k]) answer--;
            }
            Console.WriteLine(answer);
        }
    }
}