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: Accepted)

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

max = n - k + 1

p_count = 0

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

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

	t_p = p[i]
}

if count >= k then
	p_count += 1
end

min_q = []
max_q = []
del = 0

w = k - 1

(0...p.size).each{ |i|
#	print i, min_q, max_q, "\n"

	if i >= k && p[i] > max_q[0] && p[i - k] < min_q[0] then
		del += 1
	end

	if i >= w then
		if min_q[0] == p[i - w] then
			min_q.shift
		end
		if max_q[0] == p[i - w] then
			max_q.shift
		end
	end
	
	min_i = min_q.bsearch_index{ |x| x > p[i] }
	if min_i != nil then
		min_q.pop(min_q.size - min_i)
	end
	max_i = max_q.bsearch_index{ |x| x < p[i] }
	if max_i != nil then
		max_q.pop(max_q.size - max_i)
	end

	min_q.push(p[i])
	max_q.push(p[i])
}

#print del, p_count, "\n"
puts max - [p_count - 1, 0].max - del