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)

# Studying https://atcoder.jp/contests/agc038/submissions/7680063
N, K, *P = $<.read.split.map(&:to_i)

pm, n = 0, 0
i, QMin, QMax = 0, [0], [0]
until (i+=1) == N
	p = P[i]

	min_gone = QMin[0] == i-K
	if p < P[QMin[0]]
		QMin.clear
	else
		QMin.pop while p < P[QMin[-1]]
	end
	QMin << i
	QMin.shift if QMin[0] == i-K

	if P[QMax[0]] < p
		QMax.clear
	else
		QMax.pop while P[QMax[-1]] < p
	end
	QMax << i
	QMax.shift if QMax[0] == i-K
	max_entered = QMax[0] == i

	next if i < K-1

	if QMin.size == K
		pm += 1
	elsif ! min_gone or ! max_entered
		n += 1
	end
end

p n+[pm,1].min