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 OCaml (4.02.3) (judge verdict: Wrong Answer)

Scanf.scanf "%d %d" (fun n k ->
    let p = Array.init n (fun _ -> Scanf.scanf " %d" (fun p -> p)) in
    let module S = Set.Make (struct type t = int let compare = compare end) in

    let grp = Array.make n 0 in

    let rec loop i prev cur =
        if i = n then () else
            let cur = if p.(i) > prev then cur else cur + 1 in
            let () = grp.(i) <- cur in
            loop (i + 1) p.(i) cur
    in
    loop 1 p.(0) 0;

    let par = Array.init (n - k + 2) (fun i -> i) in
    let rec root x =
        if x = par.(x) then x else
            let r = root par.(x) in
            let () = par.(x) <- r in
            r
    in
    let merge a b =
        if root a <> root b then par.(par.(b)) <- par.(a)
    in

    let e = n - k + 1 in

    let rec loop i set =
        if grp.(i) = grp.(i + k - 1) then merge i e;
        if i + k = n then () else
            let cmi = S.min_elt set in
            let cmx = S.max_elt set in
            let set = S.remove p.(i) set in
            let set = S.add p.(i + k) set in
            let nmi = S.min_elt set in
            let nmx = S.max_elt set in

            if grp.(i) <> grp.(i + k - 1) && cmi = nmi && cmx = nmx then merge i (i + 1);
            loop (i + 1) set
    in
    let init =
        let rec loop i set =
            if i = k then set else loop (i + 1) (S.add p.(i) set)
        in
        loop 0 S.empty
    in
    loop 0 init;
    let rec loop i set =
        if i + k > n then S.cardinal set else
            loop (i + 1) (S.add (root i) set)
    in
    loop 0 S.empty |> Printf.printf "%d\n"
)