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)

n = 1
s = P[0,K].sort
pm = s == P[0,K] ? 1 : 0
(N-K).times {|i|
	min, pop, push = s[0], P[i], P[i+K]
	s.insert(s.bsearch_index{|_| push < _ }||K, push)
	s.delete_at(s.bsearch_index{|_| pop <=> _ })
	n += 1 if min != pop or push != s[-1]
	pm += 1 if s == P[i+1,K]
#p({:s=>s,:min=>min,:pop=>pop,:push=>push,:n=>n,:pm=>pm})
}

p n-[pm-1,0].max