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 B
{
	static void Main()
	{
		Func<int[]> read = () => Console.ReadLine().Split().Select(int.Parse).ToArray();
		var h = read();
		var p = read();
		int n = h[0], k = h[1];

		var c = n - k + 1;
		c -= Enumerable.Range(0, n - k).Count(i => p.Skip(i).Take(k + 1).Min() == p[i] && p.Skip(i).Take(k + 1).Max() == p[i + k]);

		int c2 = 0, t = 0, v = -1;
		for (int i = 0; i < n; i++)
		{
			if (p[i] > v)
			{
				t++;
			}
			else
			{
				if (t >= k) c2++;
				t = 1;
			}
			v = p[i];
		}
		if (t >= k) c2++;
		if (c2 > 0) c -= c2 - 1;

		Console.WriteLine(c);
	}
}