Problem:
Score : 800 points

Problem Statement

Takahashi Lake has a perimeter of L. On the circumference of the lake, there is a residence of the lake's owner, Takahashi.
Each point on the circumference of the lake has a coordinate between 0 and L (including 0 but not L), which is the distance from the Takahashi's residence, measured counter-clockwise.

There are N trees around the lake; the coordinate of the i-th tree is X_i. There is no tree at coordinate 0, the location of Takahashi's residence.

Starting at his residence, Takahashi will repeat the following action:

If all trees are burnt, terminate the process.

Specify a direction: clockwise or counter-clockwise.

Walk around the lake in the specified direction, until the coordinate of a tree that is not yet burnt is reached for the first time.

When the coordinate with the tree is reached, burn that tree, stay at the position and go back to the first step.

Find the longest possible total distance Takahashi walks during the process.

Partial Score

A partial score can be obtained in this problem:

300 points will be awarded for passing the input satisfying N \leq 2000.

Constraints

2 \leq L \leq 10^9

1 \leq N \leq 2\times 10^5

1 \leq X_1 < ... < X_N \leq L-1

All values in input are integers.

Input

Input is given from Standard Input in the following format:

L N
X_1
:
X_N

Output

Print the longest possible total distance Takahashi walks during the process.

Sample Input 1

10 3
2
7
9

Sample Output 1

15

Takahashi walks the distance of 15 if the process goes as follows:

Walk a distance of 2 counter-clockwise, burn the tree at the coordinate 2 and stay there.

Walk a distance of 5 counter-clockwise, burn the tree at the coordinate 7 and stay there.

Walk a distance of 8 clockwise, burn the tree at the coordinate 9 and stay there.

Sample Input 2

10 6
1
2
3
6
7
9

Sample Output 2

27

Sample Input 3

314159265 7
21662711
77271666
89022761
156626166
160332356
166902656
298992265

Sample Output 3

1204124749

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

#[allow(unused_macros)]
macro_rules! my_write {
  ($writer:expr, $args:expr) => {
    $writer.write($args).unwrap()
  };
  ($writer:expr, $($args:expr),*) => {
    {
      let mut buf = Vec::new();
      $(buf.write($args).unwrap();)*
      $writer.write(&buf).unwrap()
    }
  };
}

use std::io::{ stdin, stdout, Write };

#[inline(always)]
fn agc030_b() {
  let stdin  = stdin();
  let stdout = stdout();
  let mut scanner = my::Scanner::with_capacity(12, stdin.lock());
  let mut writer  = stdout.lock();
  let mut itoa    = my::ItoA::with_capacity(10);

  let l = my::atoui::<usize>(scanner.read_until(my::SP));
  let n = my::atoui::<usize>(scanner.read_until(my::LF));

  let mut vec = scanner.fold(n, my::LF, Vec::with_capacity(n), | mut v, s | {
    v.push(my::atoui::<usize>(s));
    v
  });

  let mut ans = 0;
  let mut pos = 0;

  let mut i = 0;
  let mut j = vec.len() - 1;
  let mut x = 0;
  let mut y = 0;


  if vec[i] >= l - vec[j] {
    pos = vec.remove(0);
    ans += pos;
  } else {
    ans += l - vec[j];
    pos = vec.remove(j);
  }
  if vec.len() > 0 {
    j = vec.len() - 1;
  }

  while vec.len() > 0 {
    if vec[i] < pos {
      x = l - pos + vec[i];
      y = pos - vec[j];
    } else {
      x = vec[i] - pos;
      y = l - vec[j] + pos;
    }

    if x >= y {
      pos  = vec.remove(0);
      ans += x;
    } else {
      ans += y;
      pos = vec.remove(j);
    }
    if vec.len() > 0 {
      j = vec.len() - 1;
    }
  }

  my_write!(writer, itoa.from_usize(ans), b"\n");
  writer.flush().unwrap();
}

fn main() {
  agc030_b();
}

//------------------------------------------------------------------------
mod my {
  use std::fmt::Debug;
  use std::ops::{ Add, Sub, Mul, Div, Rem, Neg };
  use std::mem::swap;
  use std::hash::{ Hasher, BuildHasher };

  #[allow(dead_code)]
  pub const SP: u8 = b' ';
  #[allow(dead_code)]
  pub const LF: u8 = b'\n';

  //----------------------------------------------------------------------
  pub struct MyHasher(u64);

  impl Default for MyHasher {
    #[inline(always)]
    fn default() -> Self {
      MyHasher(0x00)
    }
  }

  impl BuildHasher for MyHasher {
    type Hasher = MyHasher;

    #[inline(always)]
    fn build_hasher(&self) -> Self::Hasher {
      Self::Hasher::default()
    }
  }

  impl Hasher for MyHasher {
    #[inline(always)]
    fn finish(&self) -> u64 {
      self.0
    }

    #[inline(always)]
    fn write(&mut self, bytes: &[u8]) {
      self.0 = 0;
      for i in 0..bytes.len() {
        self.0 ^= (bytes[i] as u64) << (8 * (i % 8));
      }
    }
  }

  //----------------------------------------------------------------------
  #[allow(dead_code)]
  #[inline(always)]
  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 {
      swap(&mut x.0, &mut x.1);
    }
    if y.0 > y.1 {
      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)]
  #[inline(always)]
  pub fn rotate_right<T>(ary: &mut [T])
    where T: Copy +
             Debug
  {
    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)]
  #[inline(always)]
  pub fn rotate_left<T>(ary: &mut [T])
    where T: Copy +
             Debug
  {
    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;
  }

  //----------------------------------------------------------------------
  #[allow(dead_code)]
  #[inline(always)]
  pub fn is_ascii_digit(b: u8) -> bool {
    if b >= b'0' && b <= b'9' {
      true
    } else {
      false
    }
  }

  #[allow(dead_code)]
  #[inline(always)]
  pub fn is_ascii_uppercase(b: u8) -> bool {
    if b >= b'A' && b <= b'Z' {
      true
    } else {
      false
    }
  }

  #[allow(dead_code)]
  #[inline(always)]
  pub fn is_ascii_lowercase(b: u8) -> bool {
    if b >= b'a' && b <= b'z' {
      true
    } else {
      false
    }
  }

  #[allow(dead_code)]
  #[inline(always)]
  pub fn is_ascii_alphabetic(b: u8) -> bool {
    if is_ascii_uppercase(b) || is_ascii_lowercase(b) {
      true
    } else {
      false
    }
  }

  #[allow(dead_code)]
  #[inline(always)]
  pub fn to_ascii_lowercase(b: u8) -> u8 {
    if is_ascii_uppercase(b) {
      b + 0x20
    } else {
      b
    }
  }

  #[allow(dead_code)]
  #[inline(always)]
  pub fn to_ascii_uppercase(b: u8) -> u8 {
    if is_ascii_lowercase(b) {
      b - 0x20
    } else {
      b
    }
  }

  //----------------------------------------------------------------------
  #[allow(dead_code)]
  #[inline(always)]
  pub fn gcd<T>(mut x: T, mut y: T) -> T
    where T: Rem<Output=T> +
             Default +
             PartialEq +
             Copy +
             Debug
  {
    let zero = T::default();
    if x == zero { return y; }

    while y != zero {
      let tmp = x % y;
      x = y;
      y = tmp;
    }

    x
  }

  #[allow(dead_code)]
  #[inline(always)]
  pub fn lcm<T>(x: T, y: T) -> T
    where T: Mul<Output=T> +
             Div<Output=T> +
             Rem<Output=T> +
             Default +
             PartialEq +
             Copy +
             Debug
  {
    x * y / gcd(x, y)
  }

  //----------------------------------------------------------------------
  #[allow(dead_code)]
  #[inline(always)]
  pub fn atoui<T>(s: &[u8]) -> T
    where T: Add<Output=T> +
             Sub<Output=T> +
             Mul<Output=T> +
             Default +
             From<u8> +
             Debug
  {
    let mut n = T::default();
    if s.len() == 0 {
      return n;
    }

    let mut i = 0;
    if s[i] == b'+' {
      i += 1;
    }

    for b in &s[i..] {
      n = (n * T::from(10)) + T::from(b - b'0');
    }

    n
  }

  #[allow(dead_code)]
  #[inline(always)]
  pub fn atoi<T>(s: &[u8]) -> T
    where T: Add<Output=T> +
             Sub<Output=T> +
             Mul<Output=T> +
             Neg<Output=T> +
             Default +
             From<u8> +
             Debug
  {
    let mut n = T::default();
    if s.len() == 0 {
      return n;
    }

    let mut i        = 0;
    let mut negative = false;
    if s[i] == b'+' {
      i += 1;
    } else if s[i] == b'-' {
      i += 1;
      negative = true;
    }

    for b in &s[i..] {
      n = (n * T::from(10)) + T::from(b - b'0');
    }

    if negative {
      n.neg()
    } else {
      n
    }
  }

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

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

    (int, $($name:ident => $_type:ty),*) => {$(
      #[allow(dead_code)]
      #[inline(always)]
      pub fn $name(&mut self, mut n: $_type) -> &[u8] {
        self.buf.clear();
        if n == 0 {
          self.buf.push(b'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 + b'0');
          n /= 10;
        }
        if negative {
          self.buf.push(b'-');
        }
        self.buf.reverse();
        self.buf.as_slice()
      }
    )*};
  }

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

  impl ItoA {
    #[allow(dead_code)]
    #[inline(always)]
    pub fn with_capacity(cap: usize) -> Self {
      ItoA {
        buf: Vec::with_capacity(cap),
      }
    }

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

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

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

  impl<R> Scanner<R>
    where R: ::std::io::BufRead
  {
    #[allow(dead_code)]
    #[inline(always)]
    pub fn with_capacity(cap: usize, reader: R) -> Self {
      Scanner {
        reader: reader,
        buf   : Vec::with_capacity(cap),
      }
    }

    //--------------------------------------------------------------------
    #[allow(dead_code)]
    #[inline(always)]
    pub fn into_inner(self) -> R {
      self.reader
    }

    #[allow(dead_code)]
    #[inline(always)]
    pub fn resize(&mut self, len: usize, val: u8) {
      self.buf.resize(len, val);
    }

    //--------------------------------------------------------------------
    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_until(&mut self, delim: u8) -> &[u8] {
      self.buf.clear();
      let mut len = self.reader.read_until(delim, &mut self.buf).unwrap();
      if len == 0 {
        return self.buf.as_slice();
      }

      len -= 1;
      if self.buf[len] == delim {
        self.buf.truncate(len);
      }
      self.buf.as_slice()
    }

    //--------------------------------------------------------------------
    #[allow(dead_code)]
    #[inline(always)]
    pub fn for_each<F>(&mut self, n: usize, delim: u8, mut func: F)
      where F: FnMut(&[u8])
    {
      for _ in 0..n - 1 {
        func(self.read_until(delim));
      }
      func(self.read_until(LF))
    }

    #[allow(dead_code)]
    #[inline(always)]
    pub fn fold<B, F>(&mut self, n: usize, delim: u8, mut init: B, mut func: F) -> B
      where F: FnMut(B, &[u8]) -> B
    {
      for _ in 0..n - 1 {
        init = func(init, self.read_until(delim));
      }
      func(init, self.read_until(LF))
    }
  } // impl<R> Scanner<R>

} // mod my