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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars, Usize1};
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::ops::*;
#[derive(Clone, Debug, Default)]
struct Struct;


//#[proconio::fastout]
fn main() {
    input! {
        n: usize,
        k: usize,
        p: [usize;n],
    }

    let mut sorted = BTreeSet::new();
    
    for i in 0..k {
        sorted.insert(p[i]);
    }
    let mut ans = 1;

    for i in 0..n-k {
        let mut r = sorted.range(0..n);
        let l = *r.next().unwrap();
        let h = *r.next_back().unwrap();
        if p[i] == l && p[i+k] >= h {
            // i..i+k のソート結果と i+1..i+1+k のソート結果が同じだ
        } else {
            ans += 1;
        }
        sorted.remove(&p[i]);
        sorted.insert(p[i+k]);
    }

    // ソートしても元の文字列と同じになる場合の重複を除く
    let mut sorted_len = 1;
    let mut ct = 0;
    for i in 1..n {
        if p[i-1] < p[i] {
            sorted_len += 1;
            if sorted_len == k {
                ct += 1;
            }
        } else {
            sorted_len = 1;
        }
    }
    //println!("{}", ct);

    if ct != 0 {
        ans -= ct-1;
    }

    println!("{}", ans);
}