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

ret = 0
sorted_added = false
pre_min = nil
pre_max = nil
sub = []
(0..N-K).each_with_index do |e, i|
    no_count = false
    if i > 0 && pre_min == array[i-1] && pre_max <= array[i+K-1]
        no_count = true
    end
    if sub.empty?
        sub = array.slice(i..(i+K-1)).sort
    else
        sub.shift
        ins_index = sub.bsearch_index {|x| x >= array[i+K-1] }
        if ins_index
            sub.insert(ins_index, array[i+K-1])
        else
            sub.push(array[i+K-1])
        end
    end
    pre_min = sub[0]
    pre_max = sub[K-1]
    ret += 1 if !no_count
end
count = 0
(0..(N-2)).each_with_index do |e, i|
    if array[i] <= array[i+1]
        count += 1
        if count >= K
            ret -= 1
        end
    else
        count = 0
    end
end
puts ret