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)
q = gets.split.map(&:to_i)
c = 1
ff = true
(n-k).times do |i|
  unless q[i] < q[i+1..i+k-1].min && q[i+1..i+k-1].max < q[i+k]
    f = true
    (k-1).times do |j|
      unless q[i+1+j] < q[i+2+j]
        f = false
        break
      end
    end
    if !f
      c += 1
    end
    if ff && f
      ff = false
      c += 1
    end
  end
end
p c