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 Ruby (2.3.3) (judge verdict: Wrong Answer)

n,k = gets.split.map &:to_i
p = gets.split.map &:to_i

max = n - k + 1

p_count = 0
del = 0

count = 1
t_p = p[0]
start_i = 0
a = []

(0...p.size).each{ |i|
	if p[i] > t_p then
		count += 1
	else
		a << [start_i, i - 1]
		if count >= k then
			p_count += 1
			del += count - k
		end
		count = 1
		start_i = i
	end

	t_p = p[i]
}

a << [start_i, p.size - 1]
if count >= k then
	p_count += 1
	del += count - k
end

a.each_cons(2){ |x|
	if x[1][0] - x[0][0] >= k && x[1][1] - x[0][1] >= k then
		del += 1
	end
}

puts max - p_count - del