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: Accepted)

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*);
    }
}

#[allow(unused_imports)]
use std::cmp::{min, max};
#[allow(unused_imports)]
use std::io::{stdout, stdin, BufWriter, Write};

#[derive(Debug)]
pub struct UnionFind {
    par: Vec<usize>,
}
impl UnionFind {
    pub fn new(n: usize) -> UnionFind {
        let mut vec = vec![0; n];
        for i in 0..n {
            vec[i] = i;
        }
        UnionFind { par: vec }
    }
    pub fn find(&mut self, x: usize) -> usize {
        if x == self.par[x] {
            x
        } else {
            let par = self.par[x];
            let res = self.find(par);
            self.par[x] = res;
            res
        }
    }
    pub fn same(&mut self, a: usize, b: usize) -> bool {
        self.find(a) == self.find(b)
    }
    pub fn unite(&mut self, a: usize, b: usize) {
        let apar = self.find(a);
        let bpar = self.find(b);
        self.par[apar] = bpar;
    }
}

pub mod ds {
    use std::cmp::{min, PartialOrd};
    use std::ops::{AddAssign, Sub};
    #[derive(Debug)]
    pub struct BIT<T> {
        size: usize,
        data: Vec<T>,
    }
    impl<T> BIT<T>
    where
        T: Copy + AddAssign + Sub<Output = T> + PartialOrd + From<i32>,
    {
        pub fn new(size: usize) -> Self {
            let buf_size = size.next_power_of_two();
            BIT {
                size: size,
                data: vec![T::from(0 as i32); buf_size + 1],
            }
        }
        #[doc = " [l, r) l,r: 1-indexed"]
        pub fn sum_between(&self, l: usize, r: usize) -> T {
            self.sum(r - 1) - self.sum(l - 1)
        }
        #[doc = " i: 1-indexed but returns 0 if i=0 is given."]
        pub fn sum(&self, i: usize) -> T {
            let mut i = i as i32;
            let mut ret = T::from(0 as i32);
            while i > 0 {
                ret += self.data[i as usize];
                i -= i & -i;
            }
            ret
        }
        #[doc = " i: 1-indexed"]
        pub fn add(&mut self, i: usize, value: T) {
            assert!(i > 0 && i <= self.size);
            let n = self.data.len() as i64;
            let mut i = i as i64;
            while i <= n - 1 {
                self.data[i as usize] += value;
                i += i & -i;
            }
        }
        pub fn lower_bound(&self, mut value: T) -> usize {
            let zero = T::from(0i32);
            if value <= zero {
                return 0;
            }
            let n = self.data.len();
            let mut x = 0;
            let mut k = n - 1;
            while k > 0 {
                if x + k <= n - 1 && self.data[x + k] < value {
                    value = value - self.data[x + k];
                    x += k;
                }
                k /= 2;
            }
            x = min(x, self.size);
            x + 1
        }
    }
}

use ds::BIT;

fn main() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {
        ($($format:tt)*) => (write!(out,$($format)*).unwrap());
    }

    input!{
      n: usize,
      k: usize,
      ps: [usize; n],
    }

    let mut uf = UnionFind::new(n-k+1);
    let mut start = 0;
    let mut incr = None;
    for i in 1..n {
        if ps[i-1] > ps[i] {
            start = i;
        } else {
            if i-start+1 >= k {
                if let Some(idx) = incr {
                    uf.unite(idx, start);
                } else {
                    incr = Some(start);
                }
            }
        }
    }

    let mut bit = BIT::new(n);
    for i in 0..k {
        bit.add(ps[i]+1, 1i64);
    }

    for i in k..n {
        let prev2 = bit.lower_bound(2) - 1;
        let prev = ps[i-k];
        bit.add(prev+1, -1);
        bit.add(ps[i]+1, 1);

        let first = bit.lower_bound(1) - 1;
        let last = bit.lower_bound(k as _) - 1;

        // no change
        if prev2 == first && last == ps[i] {
            uf.unite(i-k, i-k+1);
        }
    }

    let mut pars = vec![];
    for i in 0..n-k+1 {
        pars.push(uf.find(i));
    }
    pars.sort();
    pars.dedup();
    puts!("{}\n", pars.len());
}