Problem:
Score : 300 points

Problem Statement

There is a sequence of length N: A_1, A_2, ..., A_N. Initially, this sequence is a permutation of 1, 2, ..., N.

On this sequence, Snuke can perform the following operation:

Choose K consecutive elements in the sequence. Then, replace the value of each chosen element with the minimum value among the chosen elements.

Snuke would like to make all the elements in this sequence equal by repeating the operation above some number of times.
Find the minimum number of operations required.
It can be proved that, Under the constraints of this problem, this objective is always achievable.

Constraints

2 \leq K \leq N \leq 100000

A_1, A_2, ..., A_N is a permutation of 1, 2, ..., N.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 ... A_N

Output

Print the minimum number of operations required.

Sample Input 1

4 3
2 3 1 4

Sample Output 1

2

One optimal strategy is as follows:

In the first operation, choose the first, second and third elements. The sequence A becomes 1, 1, 1, 4.

In the second operation, choose the second, third and fourth elements. The sequence A becomes 1, 1, 1, 1.

Sample Input 2

3 3
1 2 3

Sample Output 2

1

Sample Input 3

8 3
7 3 1 8 4 6 2 5

Sample Output 3

4

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

#![allow(unknown_lints)]
#![allow(unused_imports, unused_macros, non_snake_case, bare_trait_objects)]
#![allow(renamed_and_removed_lints, redundant_field_names)]
use std::cmp::Ordering::{self, Greater, Less};
use std::cmp::{max, min};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::error::Error;
use std::io::{self, BufReader, BufWriter, Read, Write};
use text_scanner::{scan, scan_iter, scanln, scanln_iter};

//{{{ macros missing in 1.15.1
#[macro_use]
mod macros {
    macro_rules! eprint {
        ($($t:tt)*) => {{
            use ::std::io::Write;
            let _ = write!(::std::io::stderr(), $($t)*);
        }};
    }
    macro_rules! eprintln {
        () => { eprintln!(""); };
        ($($t:tt)*) => {{
            use ::std::io::Write;
            let _ = writeln!(::std::io::stderr(), $($t)*);
        }};
    }
    macro_rules! dbg {
        ($val:expr) => {
            match $val {
                tmp => {
                    eprintln!(
                        "[{}:{}] {} = {:#?}",
                        file!(),
                        line!(),
                        stringify!($val),
                        &tmp
                    );
                    tmp
                }
            }
        };
    }
}
//}}}

fn run() {
    let n: usize = scan();
    let k: usize = scan();
    if k == n {
        println!("{}", 1);
        return;
    }
    let a: Vec<usize> = scan_iter().collect();
    let idx = a.iter().position(|&x| x == 1).unwrap();
    let left = idx;
    let right = n - 1 - idx;

    let answer = if left == 0 {
        (right + k - 2) / (k - 1)
    } else if right == 0 {
        (left + k - 2) / (k - 1)
    } else if left < k - 1 {
        1 + (max(0, right as i32 - (k - 1 - left) as i32) as usize + k - 2) / (k - 1)
    } else if right < k - 1 {
        1 + (max(0, left as i32 - (k - 1 - right) as i32) as usize + k - 2) / (k - 1)
    } else {
        (right + k - 2) / (k - 1) + (left + k - 2) / (k - 1)
    };
    println!("{}", answer);
}

fn main() {
    std::thread::Builder::new()
        .name("run".to_string())
        .stack_size(256 * 1024 * 1024)
        .spawn(run)
        .unwrap()
        .join()
        .unwrap()
}

//{{{ utils
pub mod text_scanner {
    use std;
    #[derive(Debug)]
    pub enum Error {
        IoError(std::io::Error),
        EncodingError(std::string::FromUtf8Error),
        ParseError(String),
        Eof,
    }

    impl std::fmt::Display for Error {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            match *self {
                Error::IoError(ref e) => writeln!(f, "IO Error: {}", e),
                Error::EncodingError(ref e) => writeln!(f, "Encoding Error: {}", e),
                Error::ParseError(ref e) => writeln!(f, "Parse Error: {}", e),
                Error::Eof => writeln!(f, "EOF"),
            }
        }
    }

    impl std::error::Error for Error {
        // dummy implementation for 1.15.1
        fn description(&self) -> &str {
            "description() is deprecated; use Display"
        }
    }

    pub fn read_line() -> Option<String> {
        let stdin = std::io::stdin();
        let mut stdin = stdin.lock();
        fread_line(&mut stdin).expect("IO error")
    }

    pub fn scan<T: FromTokens>() -> T {
        let stdin = std::io::stdin();
        let mut stdin = stdin.lock();
        fscan(&mut stdin).expect("IO error")
    }

    pub fn scanln<T: FromTokens>() -> T {
        let stdin = std::io::stdin();
        let mut stdin = stdin.lock();
        fscanln(&mut stdin).expect("IO error")
    }

    pub fn scan_iter<T: FromTokens>() -> ScanIter<T> {
        ScanIter {
            item_type: std::marker::PhantomData,
        }
    }

    pub fn scanln_iter<T: FromTokens>() -> ScanlnIter<T> {
        let stdin = std::io::stdin();
        let mut stdin = stdin.lock();
        let s = fread_line(&mut stdin)
            .expect("IO error")
            .unwrap_or_else(String::new);
        ScanlnIter {
            cursor: std::io::Cursor::new(s),
            item_type: std::marker::PhantomData,
        }
    }

    pub fn fread_line<R: std::io::BufRead>(r: &mut R) -> Result<Option<String>, std::io::Error> {
        let mut buf = String::new();
        let length = r.read_line(&mut buf)?;
        if let Some('\n') = buf.chars().last() {
            buf.pop();
        }
        if let Some('\r') = buf.chars().last() {
            buf.pop();
        }
        if length == 0 {
            Ok(None)
        } else {
            Ok(Some(buf))
        }
    }

    pub fn fscan<R: std::io::Read, T: FromTokens>(reader: &mut R) -> Result<T, Error> {
        let mut tokenizer = Tokenizer::new(reader);
        FromTokens::from_tokens(&mut tokenizer)
    }

    pub fn fscanln<R: std::io::BufRead, T: FromTokens>(reader: &mut R) -> Result<T, Error> {
        let s = match fread_line(reader) {
            Ok(Some(s)) => s,
            Ok(None) => return Err(Error::Eof),
            Err(e) => return Err(Error::IoError(e)),
        };
        let mut bytes = s.as_bytes();
        let mut tokenizer = Tokenizer::new(&mut bytes);
        FromTokens::from_tokens(&mut tokenizer)
    }

    pub fn fscan_iter<R: std::io::Read, T: FromTokens>(reader: &mut R) -> FscanIter<R, T> {
        FscanIter {
            tokenizer: Tokenizer::new(reader),
            item_type: std::marker::PhantomData,
        }
    }

    pub fn fscanln_iter<R: std::io::BufRead, T: FromTokens>(
        reader: &mut R,
    ) -> Result<ScanlnIter<T>, Error> {
        let s = match fread_line(reader) {
            Ok(Some(s)) => s,
            Ok(None) => "".to_string(),
            Err(e) => return Err(Error::IoError(e)),
        };
        Ok(ScanlnIter {
            cursor: std::io::Cursor::new(s),
            item_type: std::marker::PhantomData,
        })
    }

    pub struct ScanIter<T>
    where
        T: FromTokens,
    {
        item_type: std::marker::PhantomData<T>,
    }

    impl<T: FromTokens> Iterator for ScanIter<T> {
        type Item = T;

        fn next(&mut self) -> Option<Self::Item> {
            let stdin = std::io::stdin();
            let mut stdin = stdin.lock();
            let mut tokenizer = Tokenizer::new(&mut stdin);
            match FromTokens::from_tokens(&mut tokenizer) {
                Err(Error::Eof) => None,
                r => Some(r.expect("IO error")),
            }
        }
    }

    pub struct FscanIter<'a, R, T>
    where
        R: std::io::Read + 'a,
        T: FromTokens,
    {
        tokenizer: Tokenizer<'a, R>,
        item_type: std::marker::PhantomData<T>,
    }

    impl<'a, R: std::io::Read, T: FromTokens> Iterator for FscanIter<'a, R, T> {
        type Item = Result<T, Error>;

        fn next(&mut self) -> Option<Self::Item> {
            match FromTokens::from_tokens(&mut self.tokenizer) {
                Err(Error::Eof) => None,
                r => Some(r),
            }
        }
    }

    pub struct ScanlnIter<T>
    where
        T: FromTokens,
    {
        cursor: std::io::Cursor<String>,
        item_type: std::marker::PhantomData<T>,
    }

    impl<'a, T: FromTokens> Iterator for ScanlnIter<T> {
        type Item = T;

        fn next(&mut self) -> Option<Self::Item> {
            let mut tokenizer = Tokenizer::new(&mut self.cursor);
            match FromTokens::from_tokens(&mut tokenizer) {
                Err(Error::Eof) => None,
                r => Some(r.expect("IO error")),
            }
        }
    }

    pub trait FromTokens
    where
        Self: Sized,
    {
        fn from_tokens(
            tokenizer: &mut Iterator<Item = Result<String, Error>>,
        ) -> Result<Self, Error>;
    }

    macro_rules! from_tokens_primitives {
    ($($t:ty),*) => { $(
        impl FromTokens for $t {
            fn from_tokens(tokenizer: &mut Iterator<Item = Result<String, Error>>) -> Result<Self, Error> {
                let token = tokenizer.next();
                match token {
                    Some(s) => s?
                        .parse::<$t>()
                        .map_err(|e| Error::ParseError(format!("{}", e))),
                    None => Err(Error::Eof),
                }
            }
        }
    )* }
}

    from_tokens_primitives! {
        String,
        bool,
        f32,
        f64,
        isize,
        i8,
        i16,
        i32,
        i64,
        usize,
        u8,
        u16,
        u32,
        u64
    }

    impl<T1, T2> FromTokens for (T1, T2)
    where
        T1: FromTokens,
        T2: FromTokens,
    {
        fn from_tokens(
            tokenizer: &mut Iterator<Item = Result<String, Error>>,
        ) -> Result<Self, Error> {
            Ok((T1::from_tokens(tokenizer)?, T2::from_tokens(tokenizer)?))
        }
    }

    impl<T1, T2, T3> FromTokens for (T1, T2, T3)
    where
        T1: FromTokens,
        T2: FromTokens,
        T3: FromTokens,
    {
        fn from_tokens(
            tokenizer: &mut Iterator<Item = Result<String, Error>>,
        ) -> Result<Self, Error> {
            Ok((
                T1::from_tokens(tokenizer)?,
                T2::from_tokens(tokenizer)?,
                T3::from_tokens(tokenizer)?,
            ))
        }
    }

    impl<T1, T2, T3, T4> FromTokens for (T1, T2, T3, T4)
    where
        T1: FromTokens,
        T2: FromTokens,
        T3: FromTokens,
        T4: FromTokens,
    {
        fn from_tokens(
            tokenizer: &mut Iterator<Item = Result<String, Error>>,
        ) -> Result<Self, Error> {
            Ok((
                T1::from_tokens(tokenizer)?,
                T2::from_tokens(tokenizer)?,
                T3::from_tokens(tokenizer)?,
                T4::from_tokens(tokenizer)?,
            ))
        }
    }

    impl<T1, T2, T3, T4, T5> FromTokens for (T1, T2, T3, T4, T5)
    where
        T1: FromTokens,
        T2: FromTokens,
        T3: FromTokens,
        T4: FromTokens,
        T5: FromTokens,
    {
        fn from_tokens(
            tokenizer: &mut Iterator<Item = Result<String, Error>>,
        ) -> Result<Self, Error> {
            Ok((
                T1::from_tokens(tokenizer)?,
                T2::from_tokens(tokenizer)?,
                T3::from_tokens(tokenizer)?,
                T4::from_tokens(tokenizer)?,
                T5::from_tokens(tokenizer)?,
            ))
        }
    }

    impl<T1, T2, T3, T4, T5, T6> FromTokens for (T1, T2, T3, T4, T5, T6)
    where
        T1: FromTokens,
        T2: FromTokens,
        T3: FromTokens,
        T4: FromTokens,
        T5: FromTokens,
        T6: FromTokens,
    {
        fn from_tokens(
            tokenizer: &mut Iterator<Item = Result<String, Error>>,
        ) -> Result<Self, Error> {
            Ok((
                T1::from_tokens(tokenizer)?,
                T2::from_tokens(tokenizer)?,
                T3::from_tokens(tokenizer)?,
                T4::from_tokens(tokenizer)?,
                T5::from_tokens(tokenizer)?,
                T6::from_tokens(tokenizer)?,
            ))
        }
    }

    struct Tokenizer<'a, R: std::io::Read + 'a> {
        reader: &'a mut R,
    }

    impl<'a, R: std::io::Read> Tokenizer<'a, R> {
        pub fn new(reader: &'a mut R) -> Self {
            Tokenizer { reader: reader }
        }

        pub fn next_token(&mut self) -> Result<Option<String>, Error> {
            use std::io::Read;
            let mut token = Vec::new();
            for b in self.reader.by_ref().bytes() {
                let b = b.map_err(Error::IoError)?;
                match (is_ascii_whitespace(b), token.is_empty()) {
                    (false, _) => token.push(b),
                    (true, false) => break,
                    (true, true) => {}
                }
            }
            if token.is_empty() {
                return Ok(None);
            }
            String::from_utf8(token)
                .map(Some)
                .map_err(Error::EncodingError)
        }
    }

    impl<'a, R: std::io::Read> Iterator for Tokenizer<'a, R> {
        type Item = Result<String, Error>;
        fn next(&mut self) -> Option<Self::Item> {
            match self.next_token() {
                Ok(Some(s)) => Some(Ok(s)),
                Ok(None) => None,
                Err(e) => Some(Err(e)),
            }
        }
    }

    fn is_ascii_whitespace(b: u8) -> bool {
        // Can use u8::is_ascii_whitespace once removing support of 1.15.1
        match b {
            b'\t' | b'\n' | b'\x0C' | b'\r' | b' ' => true,
            _ => false,
        }
    }
}

pub trait SetMinMax {
    fn set_min(&mut self, v: Self) -> bool;
    fn set_max(&mut self, v: Self) -> bool;
}

impl<T> SetMinMax for T
where
    T: PartialOrd,
{
    fn set_min(&mut self, v: T) -> bool {
        *self > v && {
            *self = v;
            true
        }
    }
    fn set_max(&mut self, v: T) -> bool {
        *self < v && {
            *self = v;
            true
        }
    }
}

#[derive(PartialEq, Eq, Debug, Copy, Clone, Default, Hash)]
pub struct Reverse<T>(pub T);

impl<T: PartialOrd> PartialOrd for Reverse<T> {
    #[inline]
    fn partial_cmp(&self, other: &Reverse<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }

    #[inline]
    fn lt(&self, other: &Self) -> bool {
        other.0 < self.0
    }
    #[inline]
    fn le(&self, other: &Self) -> bool {
        other.0 <= self.0
    }
    #[inline]
    fn ge(&self, other: &Self) -> bool {
        other.0 >= self.0
    }
    #[inline]
    fn gt(&self, other: &Self) -> bool {
        other.0 > self.0
    }
}

impl<T: Ord> Ord for Reverse<T> {
    #[inline]
    fn cmp(&self, other: &Reverse<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}

#[derive(PartialEq, PartialOrd, Debug, Copy, Clone, Default)]
pub struct Num(pub f64);

impl Eq for Num {}

impl Ord for Num {
    fn cmp(&self, other: &Num) -> Ordering {
        self.0
            .partial_cmp(&other.0)
            .expect("unexpected NaN when compare")
    }
}

// See https://docs.rs/superslice/1.0.0/superslice/trait.Ext.html
pub trait SliceExt {
    type Item;

    fn lower_bound(&self, x: &Self::Item) -> usize
    where
        Self::Item: Ord;

    fn lower_bound_by<'a, F>(&'a self, f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> Ordering;

    fn lower_bound_by_key<'a, K, F>(&'a self, k: &K, f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> K,
        K: Ord;

    fn upper_bound(&self, x: &Self::Item) -> usize
    where
        Self::Item: Ord;

    fn upper_bound_by<'a, F>(&'a self, f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> Ordering;

    fn upper_bound_by_key<'a, K, F>(&'a self, k: &K, f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> K,
        K: Ord;
}

impl<T> SliceExt for [T] {
    type Item = T;

    fn lower_bound(&self, x: &Self::Item) -> usize
    where
        T: Ord,
    {
        self.lower_bound_by(|y| y.cmp(x))
    }

    fn lower_bound_by<'a, F>(&'a self, mut f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> Ordering,
    {
        let s = self;
        let mut size = s.len();
        if size == 0 {
            return 0;
        }
        let mut base = 0usize;
        while size > 1 {
            let half = size / 2;
            let mid = base + half;
            let cmp = f(unsafe { s.get_unchecked(mid) });
            base = if cmp == Less { mid } else { base };
            size -= half;
        }
        let cmp = f(unsafe { s.get_unchecked(base) });
        base + (cmp == Less) as usize
    }

    fn lower_bound_by_key<'a, K, F>(&'a self, k: &K, mut f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> K,
        K: Ord,
    {
        self.lower_bound_by(|e| f(e).cmp(k))
    }

    fn upper_bound(&self, x: &Self::Item) -> usize
    where
        T: Ord,
    {
        self.upper_bound_by(|y| y.cmp(x))
    }

    fn upper_bound_by<'a, F>(&'a self, mut f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> Ordering,
    {
        let s = self;
        let mut size = s.len();
        if size == 0 {
            return 0;
        }
        let mut base = 0usize;
        while size > 1 {
            let half = size / 2;
            let mid = base + half;
            let cmp = f(unsafe { s.get_unchecked(mid) });
            base = if cmp == Greater { base } else { mid };
            size -= half;
        }
        let cmp = f(unsafe { s.get_unchecked(base) });
        base + (cmp != Greater) as usize
    }

    fn upper_bound_by_key<'a, K, F>(&'a self, k: &K, mut f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> K,
        K: Ord,
    {
        self.upper_bound_by(|e| f(e).cmp(k))
    }
}

//}}}