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: Accepted)

// ternary operation
#[allow(unused_macros)]
macro_rules! _if {
  ($_test:expr, $_then:expr, $_else:expr) => {
    if $_test { $_then } else { $_else }
  };
  ($_test:expr, $_pat:pat, $_then:expr, $_else:expr) => {
    match $_test {
      $_pat => $_then,
      _     => $_else
    }
  };
}

use std::io::{ stdin, stdout, BufWriter, Write, BufReader };
use my::WriteWithDelim;

fn arc099_a() {
  let stdin = stdin();
  let mut reader = my::ByteReader::with_capacity(8, BufReader::new(stdin.lock()));

  let stdout = stdout();
  let mut writer = BufWriter::new(stdout.lock());
  let mut i2b = my::Int2Byte::with_capacity(8);

  let n = reader.read_uint_until_sp::<usize>() - 1;
  let k = reader.read_uint_until_lf::<usize>() - 1;

  let ans = (n + k - 1) / k;

  writer.write_lf(i2b.from_usize(ans));
  writer.flush().unwrap();
}

fn main() {
  arc099_a();
}

//------------------------------------------------------------------------
mod my {

  #[allow(dead_code)]
  pub fn rotate_right(ary: &mut [u8]) {
    if ary.len() <= 1 {
      return;
    }

    let len = ary.len() - 1;
    let tmp = ary[len];
    for i in 0..len {
      ary[len - i] = ary[len - i - 1];
    }
    ary[0] = tmp;
  }

  #[allow(dead_code)]
  pub fn rotate_left(ary: &mut [u8]) {
    if ary.len() <= 1 {
      return;
    }

    let len = ary.len() - 1;
    let tmp = ary[0];
    for i in 0..len {
      ary[i] = ary[i + 1];
    }
    ary[len] = tmp;
  }

  //----------------------------------------------------------------------
  const PLUS_SIGN : u8 = b'+';
  const MINUS_SIGN: u8 = b'-';
  const ASCII_0   : u8 = b'0';
  const ASCII_9   : u8 = b'9';

  const SP        : u8 = b' ';
  const LF        : u8 = b'\n';

  #[allow(dead_code)]
  pub fn is_ascii_digit(b: u8) -> bool {
    _if!(b >= ASCII_0 && b <= ASCII_9,
      true,
      false)
  }

  #[allow(dead_code)]
  pub fn is_ascii_uppercase(b: u8) -> bool {
    _if!(b >= b'A' && b <= b'Z',
      true,
      false)
  }

  #[allow(dead_code)]
  pub fn is_ascii_lowercase(b: u8) -> bool {
    _if!(b >= b'a' && b <= b'z',
      true,
      false)
  }

  #[allow(dead_code)]
  pub fn is_ascii_alphabetic(b: u8) -> bool {
    _if!(is_ascii_uppercase(b) || is_ascii_lowercase(b),
      true,
      false)
  }

  #[allow(dead_code)]
  pub fn to_ascii_lowercase(mut b: u8) -> u8 {
    if is_ascii_uppercase(b) {
      b += 0x20;
    }
    b
  }

  #[allow(dead_code)]
  pub fn to_ascii_uppercase(mut b: u8) -> u8 {
    if is_ascii_lowercase(b) {
      b -= 0x20;
    }
    b
  }

  //----------------------------------------------------------------------
  macro_rules! pub_fn_Int2Byte_from_ty {
    (uint, $($name:ident => $_type:ty),*) => {$(
      #[allow(dead_code)]
      pub fn $name(&mut self, mut n: $_type) -> &[u8] {
        self.buf.clear();
        if n == 0 {
          self.buf.push(ASCII_0);
          return self.buf.as_slice();
        }

        while n > 0 {
          self.buf.push((n % 10) as u8 + ASCII_0);
          n /= 10;
        }
        self.buf.reverse();
        self.buf.as_slice()
      }
    )*};

    (int, $($name:ident => $_type:ty),*) => {$(
      #[allow(dead_code)]
      pub fn $name(&mut self, mut n: $_type) -> &[u8] {
        self.buf.clear();
        if n == 0 {
          self.buf.push(ASCII_0);
          return self.buf.as_slice();
        }

        let mut negative = false;
        if n.is_negative() {
          negative = true;
          n = n.abs();
        }

        while n > 0 {
          self.buf.push((n % 10) as u8 + ASCII_0);
          n /= 10;
        }
        if negative {
          self.buf.push(MINUS_SIGN);
        }
        self.buf.reverse();
        self.buf.as_slice()
      }
    )*};
  }

  #[derive(Debug)]
  pub struct Int2Byte {
    buf: Vec<u8>,
  }

  impl Int2Byte {
    #[allow(dead_code)]
    pub fn new() -> Self {
      Int2Byte {
        buf: Vec::new(),
      }
    }

    #[allow(dead_code)]
    pub fn with_capacity(capa: usize) -> Self {
      Int2Byte {
        buf: Vec::with_capacity(capa),
      }
    }

    pub_fn_Int2Byte_from_ty!(
      uint,
      from_usize => usize,
      from_u8    => u8,
      from_u16   => u16,
      from_u32   => u32,
      from_u64   => u64
    );

    pub_fn_Int2Byte_from_ty!(
      int,
      from_isize => isize,
      from_i8    => i8,
      from_i16   => i16,
      from_i32   => i32,
      from_i64   => i64
    );
  } // impl Int2Byte

  //----------------------------------------------------------------------
  use std::io::{ BufRead, BufWriter, Write };
  use std::fmt::Debug;
  use std::ops::{ Add, Sub, Mul, Neg, Rem };
  use std::str::{ self, FromStr };
  use std::mem;

  //----------------------------------------------------------------------
  #[allow(dead_code)]
  pub fn intersection<T>(mut x: (T, T), mut y: (T, T)) -> Option<(T, T)>
    where T: PartialOrd +
             Copy +
             Debug
  {
    if x.0 > x.1 {
      mem::swap(&mut x.0, &mut x.1);
    }
    if y.0 > y.1 {
      mem::swap(&mut y.0, &mut y.1);
    }

    if x.0 >= y.1 || x.1 <= y.0 {
      return None;
    }

    if x.0 < y.0 {
      x.0 = y.0;
    }
    if x.1 > y.1 {
      x.1 = y.1;
    }

    Some(x)
  }

  #[allow(dead_code)]
  pub fn gcd<T>(x: T, y: T) -> T
    where T: Rem<Output=T> +
             Default +
             PartialEq +
             Copy +
             Debug
  {
    _if!(y == T::default(),
      x,
      gcd(y, x % y))
  }

  //----------------------------------------------------------------------
  pub trait WriteWithDelim {
    fn write_delim(&mut self, buf: &[u8], delim: &[u8]) -> usize;
    fn write_sp(&mut self, buf: &[u8]) -> usize;
    fn write_lf(&mut self, buf: &[u8]) -> usize;
  }

  impl<W> WriteWithDelim for BufWriter<W>
    where W: Write
  {
    #[allow(dead_code)]
    fn write_delim(&mut self, buf: &[u8], delim: &[u8]) -> usize
    {
      self.write(buf).unwrap() +
      self.write(delim).unwrap()
    }

    #[allow(dead_code)]
    fn write_sp(&mut self, buf: &[u8]) -> usize
    {
      self.write_delim(buf, b" ")
    }

    #[allow(dead_code)]
    fn write_lf(&mut self, buf: &[u8]) -> usize
    {
      self.write_delim(buf, b"\n")
    }
  } // impl<W> WriteWithDelim for BufWriter<W>

  //----------------------------------------------------------------------

  #[allow(dead_code)]
  #[derive(Debug)]
  pub enum Direction {
    Horizontal,
    Vertical
  }

  #[derive(Debug)]
  pub struct ByteReader<R> {
    reader: R,
    buf   : Vec<u8>,
  }

  impl<R> ByteReader<R>
    where R: BufRead
  {
    #[allow(dead_code)]
    pub fn new(reader: R) -> Self {
      ByteReader {
        reader: reader,
        buf   : Vec::new(),
      }
    }

    #[allow(dead_code)]
    pub fn with_capacity(capa: usize, reader: R) -> Self {
      ByteReader {
        reader: reader,
        buf   : Vec::with_capacity(capa),
      }
    }

    //--------------------------------------------------------------------
    #[allow(dead_code)]
    pub fn read_1byte(&mut self) -> Option<u8> {
      self.buf.resize(1, 0);
      _if!(self.reader.read(&mut self.buf).unwrap() != 0,
        Some(self.buf[0]),
        None)
    }

    //--------------------------------------------------------------------
    fn read_until(&mut self, delim: u8) -> usize {
      self.buf.clear();
      self.reader.read_until(delim, &mut self.buf).unwrap()
    }

    #[allow(dead_code)]
    pub fn read_until_lf(&mut self) -> &[u8] {
      self.read_until(LF);
      self.buf.as_slice()
    }

    #[allow(dead_code)]
    pub fn read_until_sp(&mut self) -> &[u8] {
      self.read_until(SP);
      self.buf.as_slice()
    }

    //--------------------------------------------------------------------
    #[allow(dead_code)]
    pub fn read_byte_until_lf(&mut self) -> Vec<u8> {
      self.read_until(LF);
      let len = self.buf.len() - 1;
      if self.buf[len] == LF {
        self.buf.truncate(len);
      }
      self.buf.clone()
    }

    #[allow(dead_code)]
    pub fn read_string_until_lf(&mut self) -> String {
      unsafe { String::from_utf8_unchecked(self.read_byte_until_lf()) }
    }

    //--------------------------------------------------------------------
    fn parse_int<T>(&self) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Neg<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let len = self.buf.len();
      let mut i = 0;
      let mut n = T::default();
      let mut minus = false;

      if self.buf[i] == MINUS_SIGN {
        minus = true;
        i += 1;
      } else if self.buf[i] == PLUS_SIGN {
        i += 1;
      }

      while i < len && is_ascii_digit(self.buf[i]) {
        n = (n * T::from(10)) + T::from(self.buf[i] - ASCII_0);
        i += 1;
      }

      _if!(minus,
        n.neg(),
        n)
    }

    fn parse_uint<T>(&self) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let len = self.buf.len();
      let mut i = 0;
      let mut n = T::default();

      if self.buf[i] == PLUS_SIGN {
        i += 1;
      }

      while i < len && is_ascii_digit(self.buf[i]) {
        n = (n * T::from(10)) + T::from(self.buf[i] - ASCII_0);
        i += 1;
      }
      n
    }

    //--------------------------------------------------------------------
    #[allow(dead_code)]
    pub fn read_int_until_delim<T>(&mut self, delim: u8) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Neg<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      self.read_until(delim);
      self.parse_int()
    }

    // s -> n
    #[allow(dead_code)]
    pub fn read_int_until_lf<T>(&mut self) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Neg<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      self.read_int_until_delim(LF)
    }

    // s -> n
    #[allow(dead_code)]
    pub fn read_int_until_sp<T>(&mut self) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Neg<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      self.read_int_until_delim(SP)
    }

    //--------------------------------------------------------------------
    #[allow(dead_code)]
    pub fn read_uint_until_delim<T>(&mut self, delim: u8) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      self.read_until(delim);
      self.parse_uint()
    }

    // s -> n
    #[allow(dead_code)]
    pub fn read_uint_until_lf<T>(&mut self) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      self.read_uint_until_delim(LF)
    }

    // s -> n
    #[allow(dead_code)]
    pub fn read_uint_until_sp<T>(&mut self) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      self.read_uint_until_delim(SP)
    }

    //--------------------------------------------------------------------

    fn from_utf8_unchecked(&mut self) -> &str {
      unsafe { str::from_utf8_unchecked(&self.buf) }
    }

    fn parse_tok<T>(&mut self) -> T
      where T: FromStr + Debug,
            <T as FromStr>::Err: Debug
    {
      self.from_utf8_unchecked()
        .trim()
        .parse()
        .unwrap()
    }

    // s -> n
    #[allow(dead_code)]
    pub fn parse_until_delim<T>(&mut self, delim: u8) -> T
      where T: FromStr + Debug,
            <T as FromStr>::Err: Debug
    {
      self.read_until(delim);
      self.parse_tok()
    }

    // s -> n
    #[allow(dead_code)]
    pub fn parse_until_lf<T>(&mut self) -> T
      where T: FromStr + Debug,
            <T as FromStr>::Err: Debug
    {
      self.parse_until_delim(LF)
    }

    // s -> n
    #[allow(dead_code)]
    pub fn parse_until_sp<T>(&mut self) -> T
      where T: FromStr + Debug,
            <T as FromStr>::Err: Debug
    {
      self.parse_until_delim(SP)
    }

    //--------------------------------------------------------------------
    #[allow(dead_code)]
    pub fn read_int_vec<T>(&mut self, n: usize, dir: Direction) -> Vec<T>
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Neg<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let delim = _if!(dir, Direction::Horizontal, SP, LF);
      let mut vec = Vec::with_capacity(n);
      for _ in 0..n - 1 {
        vec.push(self.read_int_until_delim(delim));
      }
      vec.push(self.read_int_until_delim(LF));
      vec
    }

    #[allow(dead_code)]
    pub fn read_uint_vec<T>(&mut self, n: usize, dir: Direction) -> Vec<T>
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let delim = _if!(dir, Direction::Horizontal, SP, LF);
      let mut vec = Vec::with_capacity(n);
      for _ in 0..n - 1 {
        vec.push(self.read_uint_until_delim(delim));
      }
      vec.push(self.read_uint_until_delim(LF));
      vec
    }

    // horizontal
    //
    // N
    // s1 s2 s3, ..., sN -> [n1, n2, n3, ..., nN]
    #[allow(dead_code)]
    pub fn read_int_vec_h<T>(&mut self) -> Vec<T>
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Neg<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let n: usize = self.read_uint_until_lf();
      self.read_int_vec(n, Direction::Horizontal)
    }

    // horizontal
    //
    // N
    // s1 s2 s3, ..., sN -> [n1, n2, n3, ..., nN]
    #[allow(dead_code)]
    pub fn read_uint_vec_h<T>(&mut self) -> Vec<T>
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let n: usize = self.read_uint_until_lf();
      self.read_uint_vec(n, Direction::Horizontal)
    }

    #[allow(dead_code)]
    pub fn read_uint_vec2<T>(&mut self, n: usize, m: usize) -> Vec<Vec<T>>
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let mut vec = Vec::with_capacity(n);
      for _ in 0..n {
        vec.push(self.read_uint_vec(m, Direction::Horizontal));
      }
      vec
    }

    // N M
    // s11 s12 s13 ... s1M
    // s21 s22 s23 ... s2M
    // s31 s32 s33 ... s3M
    //   :
    // sN1 sN2 sN3 ... sNM
    // -> [
    //      [n11, n12, n13, ..., n1M],
    //      [n21, n22, n23, ..., n2M],
    //      [n31, n32, n33, ..., n3M],
    //          :
    //      [nN1, nN2, nN3, ..., nNM],
    //    ]
    #[allow(dead_code)]
    pub fn read_int_vec2<T>(&mut self, n: usize, m: usize) -> Vec<Vec<T>>
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Neg<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let mut vec = Vec::with_capacity(n);
      for _ in 0..n {
        vec.push(self.read_int_vec(m, Direction::Horizontal));
      }
      vec
    }

  } // impl<R> ByteReader<R>

} // mod my