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)

def Next _N, _P, _O1, _I, o
	(_N-1).downto(0){|i|
		j = [_I[i]+1, _N].min
		j = _O1[j] while j < _N and _P[j] <= _P[i]
		o[i] = j
	}
end

def Gen _N, _P
	io = (0..._N).to_a # 0
	Next(_N, _P, io, io, io)
	o1 = io.dup # 1
	return Enumerator.new{|y|
		y << o1.dup # 1
		loop {
			Next(_N, _P, o1, io, io)
			y << io.dup # 2, 3, 4,...
		}
	}
end

RL = Gen(N, P.map{|_| -_ }).next
LU = Gen(N, P.reverse).next.map!{|i| N-1-i }.reverse!

UP = [1] * N
(N-2).downto(0){|i|
	UP[i] = P[i] < P[i+1] ? UP[i+1]+1 : 1
}
IsPM = lambda{|i|
	return K <= UP[i]
}

pm, n = IsPM[0] ? [1, 0] : [0, 1]
(N-K).times{|i|
#p({:i=>i, :IsPM=>IsPM[i+1], :RU=>RU[i], :LU=>LU[i+K]})
	if IsPM[i+1]
		pm += 1
	elsif RL[i] < i+K or i < LU[i+K]
		n += 1
	end
}

p n+[pm,1].min