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 (1.15.1) (judge verdict: Time Limit Exceeded)

use std::io::stdin;
use std::collections::HashSet;

fn main() {
    let mut st = String::new();
    stdin().read_line(&mut st).unwrap();
    let (n, k) = {
        let nk:Vec<_> = st.trim().split(" ").map(|x| x.parse::<usize>().unwrap()).collect();
        (nk[0], nk[1])
    };
    let mut st = String::new();
    stdin().read_line(&mut st).unwrap();
    let p:Vec<i32> = st.trim().split(" ").map(|x| x.parse().unwrap()).collect();
    let mut r:HashSet<Vec<i32>> = HashSet::new();
    for num in 0..(n-k+1) {
        let i = num as usize;
        let mut x:Vec<i32> = Vec::new();
        let mut y:Vec<i32> = p[i..i+k].to_vec();
        x.extend(&p[..i]);
        y.sort();
        x.extend(&y);
        x.extend(&p[i+k..]);
        r.insert(x);
    };
    println!("{}", r.len());
}