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, *P = $<.read.split.map(&:to_i)

pm, n = 0, 2-K
i, Q, min_h, min_t, max_h, max_t = 0, [0]*N, 0, 0, N-1, N-1
until (i+=1) == N
	p = P[i]

#	assert(0 <= min_h <= min_t <= max_t <= max_h < N)
	min_gone = Q[min_h] == i-K
	if p < P[Q[min_h]]
		min_h  = min_t
		min_t -= 1
	else
		min_t -= 1 while p < P[Q[min_t]]
		min_h += 1 if Q[min_h] == i-K
	end
	if P[Q[max_h]] < p
		max_h  = max_t
		max_t += 1
	else
		max_t += 1 while P[Q[max_t]] < p
		max_h -= 1 if Q[max_h] == i-K
	end
	Q[min_t+=1] = Q[max_t-=1] = i
	max_entered = Q[max_h] == i
#	assert(0 <= min_h <= min_t <= max_t <= max_h < N)

	if min_t-min_h+1 == K
		pm = 1
	elsif ! min_gone or ! max_entered
		n += 1
	end
end

p n+pm