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.chomp.split(" ").map(&:to_i)
s = gets.chomp.split(" ").map(&:to_i)

ptn = 1
kset = []
kmax = 0
kmin = n-1

s[0...k].each do |e|
  if kmax < e
    kmax = e
  end
  if kmin > e
    kmin = e
  end
  kset << e
end

(n-k).times do |i|
  addptn = false
  j = i+k
  e = s[j]
  pe = kset.shift
  if pe == kmax
    kmax = kset.max
  end
  if pe == kmin
    kmin = kset.min
  else
    addptn = true
  end
  if kmax < e
    kmax = e
  else
    addptn = true
  end
  if kmin > e
    kmin = e
  end
  kset << e
  if addptn
    ptn += 1
  end
end

print("#{ptn}")