Problem:
Score : 400 points

Problem Statement

Caracal is fighting with a monster.

The health of the monster is H.

Caracal can attack by choosing one monster. When a monster is attacked, depending on that monster's health, the following happens:

If the monster's health is 1, it drops to 0.

If the monster's health, X, is greater than 1, that monster disappears. Then, two new monsters appear, each with the health of \lfloor X/2 \rfloor.

(\lfloor r \rfloor denotes the greatest integer not exceeding r.)

Caracal wins when the healths of all existing monsters become 0 or below.

Find the minimum number of attacks Caracal needs to make before winning.

Constraints

1 \leq H \leq 10^{12}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

H

Output

Find the minimum number of attacks Caracal needs to make before winning.

Sample Input 1

2

Sample Output 1

3

When Caracal attacks the initial monster, it disappears, and two monsters appear, each with the health of 1.

Then, Caracal can attack each of these new monsters once and win with a total of three attacks.

Sample Input 2

4

Sample Output 2

7

Sample Input 3

1000000000000

Sample Output 3

1099511627775

Solution in Rust (1.15.1) (judge verdict: Runtime Error)

use std::io;
use io_ext::Reader;
use parse::ParseAll;
use std::cmp;

fn main() {
    let stdin = io::stdin();
    let mut r = Reader::new(stdin.lock());
    let (hp, n): (isize, usize) = r.read_line().split_whitespace().parse_all();
    let mut atk_mp: Vec<(isize, isize)> = Vec::with_capacity(n);
    for _ in 0..n {
        atk_mp.push(r.read_line().split_whitespace().parse_all());
    }
    let atk_mp = clean(&mut atk_mp);
    let a = answer(hp, &atk_mp);
    println!("{}", a);
}

fn main2() {
    // let hp = 100;
    // let mut atk_mp = [(1, 1), (2, 3), (3, 9), (4, 27), (5, 81), (6, 243)];
    
    // let hp = 9;
    // let mut atk_mp = [(8, 3), (4, 2), (2, 1)];

    let hp = 9999;
    let mut atk_mp = [(540, 7550), (691, 9680), (700, 9790), (510, 7150), (415, 5818), (551, 7712), (587, 8227), (619, 8671), (588, 8228), (176, 2461)];

    let atk_mp = clean(&mut atk_mp);
    let a = answer(hp, &atk_mp);
    println!("{}", a);
}

fn clean(atk_mp: &mut[(isize, isize)]) -> Vec<(isize, isize)> {
    if atk_mp.is_empty() {
        return Vec::new();
    }

    atk_mp.sort_by_key(|&(atk, _)| -atk);
    atk_mp.sort_by_key(|&(_, mp)| mp);
    let mut ret = Vec::new();
    'outer: for &(atk, mp) in atk_mp.iter() {
        for &(prev_atk, prev_mp) in &ret {
            if atk <= prev_atk {
                continue 'outer;
            }
            if atk <= mp / prev_mp * prev_atk {
                continue 'outer;
            }
        }
        
        ret.push((atk, mp))
    }
    ret
}

fn answer(hp: isize, atk_mp: &[(isize, isize)]) -> isize {
    if atk_mp.len() == 1 {
        let (atk, mp) = atk_mp[0];
        return (hp + atk - 1) / atk * mp;
    }

    let (atk, mp) = atk_mp[atk_mp.len() - 1];
    let n = (hp + atk - 1) / atk;
    let mut min = mp * n;
    for k in 0..n {
        let consume = answer(hp - atk * k, &atk_mp[..(atk_mp.len() - 1)]);
        min = cmp::min(min, consume + mp * k);
    }
    min
}

/// A module for easy use of io.
pub mod io_ext {
    use std::io::BufRead;

    pub struct Reader<R> {
        buf: String,
        inner: R,
    }

    impl<R> Reader<R> {
        #[inline]
        pub fn new(inner: R) -> Self {
            Reader { buf: String::new(), inner: inner }
        }

        #[inline]
        pub fn into_inner(self) -> R {
            self.inner
        }
    }

    impl<R: BufRead> Reader<R> {
        #[allow(deprecated)]
        #[inline]
        pub fn read_line(&mut self) -> &str {
            self.buf.clear();
            self.inner.read_line(&mut self.buf).unwrap_or_else(|e| panic!("{}", e));
            self.buf.trim_right()
        }
    }
}

/// Parsing Iterator.
pub mod parse {
    use std::borrow::Borrow;
    use std::str::FromStr;

    pub trait FromStrIterator {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(i: I) -> Self;
    }

    pub trait ParseAll {
        fn parse_all<F: FromStrIterator>(self) -> F;
    }

    impl<S: Borrow<str>, I: Iterator<Item=S>> ParseAll for I {
        #[inline]
        fn parse_all<F: FromStrIterator>(self) -> F {
            F::from_str_iter(self)
        }
    }

    fn parse<S: Borrow<str>, I: Iterator<Item=S>, F: FromStr>(i: &mut I) -> F {
        i.next().unwrap_or_else(|| panic!("too few strings error")).borrow().parse().unwrap_or_else(|_| panic!("parse error"))
    }

    // To avoid conflict, this is not implemented for `A` but `(A,)`.
    impl<A: FromStr> FromStrIterator for (A, ) {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(mut i: I) -> Self {
            let a = parse(&mut i);
            if i.next().is_some() {
                panic!("too many strings error");
            }
            (a, )
        }
    }

    impl<A: FromStr, B: FromStr> FromStrIterator for (A, B) {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(mut i: I) -> Self {
            let a = parse(&mut i);
            let b = parse(&mut i);
            if i.next().is_some() {
                panic!("too many strings error");
            }
            (a, b)
        }
    }

    impl<A: FromStr, B: FromStr, C: FromStr> FromStrIterator for (A, B, C) {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(mut i: I) -> Self {
            let a = parse(&mut i);
            let b = parse(&mut i);
            let c = parse(&mut i);
            if i.next().is_some() {
                panic!("too many strings error");
            }
            (a, b, c)
        }
    }

    impl<A: FromStr, B: FromStr, C: FromStr, D: FromStr> FromStrIterator for (A, B, C, D) {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(mut i: I) -> Self {
            let a = parse(&mut i);
            let b = parse(&mut i);
            let c = parse(&mut i);
            let d = parse(&mut i);
            if i.next().is_some() {
                panic!("too many strings error");
            }
            (a, b, c, d)
        }
    }

    impl<T: FromStr> FromStrIterator for Vec<T> {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(i: I) -> Self {
            i.map(|s| s.borrow().parse().unwrap_or_else(|_| panic!("parse error"))).collect()
        }
    }
}

pub mod modulo {
    /// Returns `x` + `y` mod `modulo`.
    ///
    /// `x < modulo` and `y < modulo` must hold.
    #[inline]
    pub fn add(x: u32, y: u32, modulo: u32) -> u32 {
        debug_assert!(modulo > 0);
        debug_assert!(x < modulo && y < modulo);
        let sum = x as u64 + y as u64;
        if sum <= modulo as u64 {
            sum as u32
        } else {
            (sum as u32).wrapping_sub(modulo)
        }
    }

    /// Returns `x` - `y` mod `modulo`.
    ///
    /// `x < modulo` and `y < modulo` must hold.
    #[inline]
    pub fn sub(x: u32, y: u32, modulo: u32) -> u32 {
        debug_assert!(0 < modulo);
        debug_assert!(x < modulo && y < modulo);
        if x >= y {
            x - y
        } else {
            modulo + x - y
        }
    }

    /// Returns `x` * `y` mod `modulo`.
    #[inline]
    pub fn mul(x: u32, y: u32, modulo: u32) -> u32 {
        ((x as u64 * y as u64) % modulo as u64) as u32
    }

    /// Returns `x`^ `y` mod `modulo`.
    pub fn pow(x: u32, mut y: u32, modulo: u32) -> u32 {
        debug_assert!(0 < modulo);
        let mut p = x;
        let mut ret = 1;

        while y != 0 {
            if y & 1 == 1 {
                ret = mul(ret, p, modulo);
            }
            p = mul(p, p, modulo);
            y >>= 1;
        }
        ret
    }

    fn is_prime(x: u32) -> bool {
        let sqrt = (x as f32).sqrt() as u32;
        for factor in 2..sqrt {
            if x % factor == 0 {
                return false;
            }
        }
        true
    }

    /// Returns 1 / `x`.
    ///
    /// `modulo` must be a prime number.
    #[inline]
    fn reciprocal(x: u32, modulo: u32) -> u32 {
        debug_assert!(0 < modulo && is_prime(modulo));
        pow(x, modulo - 2, modulo)
    }

    /// Returns `x` / `y` mod `modulo`.
    ///
    /// `modulo` must be a prime number.
    #[inline]
    pub fn div(x: u32, y: u32, modulo: u32) -> u32 {
        debug_assert!(0 < modulo && is_prime(modulo));
        mul(x, reciprocal(y, modulo), modulo)
    }

    /// Returns `n`P`k` mod `modulo`.
    pub fn perm(n: u32, k: u32, modulo: u32) -> u32 {
        let mut p = 1;
        for i in 0..k {
            p = mul(p, n - i, modulo);
        }
        p
    }

    /// Returns `n`C`k` mod `modulo`.
    pub fn comb(n: u32, k: u32, modulo: u32) -> u32 {
        let num = perm(n, k, modulo);
        let mut den = 1;
        for i in 0..k {
            den = mul(den, i + 1, modulo);
        }
        div(num, den, modulo)
    }
}