Problem:
Score : 500 points

Problem Statement

We have N logs of lengths A_1,A_2,\cdots A_N.

We can cut these logs at most K times in total. When a log of length L is cut at a point whose distance from an end of the log is t (0<t<L), it becomes two logs of lengths t and L-t.

Find the shortest possible length of the longest log after at most K cuts, and print it after rounding up to an integer.

Constraints

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

0 \leq K \leq 10^9

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \cdots A_N

Output

Print an integer representing the answer.

Sample Input 1

2 3
7 9

Sample Output 1

4

First, we will cut the log of length 7 at a point whose distance from an end of the log is 3.5, resulting in two logs of length 3.5 each.

Next, we will cut the log of length 9 at a point whose distance from an end of the log is 3, resulting in two logs of length 3 and 6.

Lastly, we will cut the log of length 6 at a point whose distance from an end of the log is 3.3, resulting in two logs of length 3.3 and 2.7.

In this case, the longest length of a log will be 3.5, which is the shortest possible result. After rounding up to an integer, the output should be 4.

Sample Input 2

3 0
3 4 5

Sample Output 2

5

Sample Input 3

10 10
158260522 877914575 602436426 24979445 861648772 623690081 433933447 476190629 262703497 211047202

Sample Output 3

292638192

Solution in Rust (1.42.0) (judge verdict: Accepted)

#[allow(unused)]
use {
    std::error::Error,
    std::fmt::Debug,
    std::str::FromStr,
    std::io::prelude::*,
    std::io::{stdin, stdout, BufReader, BufWriter},
    std::collections::{HashSet, BinaryHeap},
    std::cmp::min,
};

type BoxResult<T> = Result<T, Box<dyn std::error::Error>>;

const M: usize = 1_000_000_000;

fn main() -> BoxResult<()> {
    let mut scanner = Scanner::new(stdin());
    
    let (_, k) = scanner.read_two::<usize, usize>()?;

    let vals = scanner.read_vector::<usize>()?;
    let ans = solve(k, &vals);

    println!("{}", ans);

    Ok(())
}

fn solve(k: usize, vals: &[usize]) -> usize {
    if judge(1, k, vals) {
        return 1;
    }
    let (mut l, mut r) = (1, M);
    while r - l > 1 {
        let mid = (l + r) / 2;
        if judge(mid, k, vals) {
            r = mid;
        } else {
            l = mid;
        }
    }
    r
}

fn judge(x: usize, k: usize, vals: &[usize]) -> bool {
    let mut count = 0;
    for v in vals {
        if v % x == 0 {
            count += v / x - 1;
        } else {
            count += v / x;
        }
    }
    count <= k
}

pub struct Scanner<R> {
    reader: BufReader<R>,
    buffer: String,
}
impl<R> Scanner<R>
where
    R: Read,
{
    pub fn new(inner: R) -> Scanner<R> {
        let reader = BufReader::new(inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
    pub fn with_capacity(capacity: usize, inner: R) -> Scanner<R> {
        let reader = BufReader::with_capacity(capacity, inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
    pub fn read_line(&mut self) -> BoxResult<String> {
        self.reader.read_line(&mut self.buffer)?;
        let cloned = self.buffer.trim().to_string();
        self.buffer.clear();
        Ok(cloned)
    }
 
    pub fn read<T>(&mut self) -> BoxResult<T>
    where
        T: FromStr,
        T::Err: Debug + Error + 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed = self.buffer.trim().parse()?;
        self.buffer.clear();
        Ok(parsed)
    }
    pub fn read_two<T, U>(&mut self) -> BoxResult<(T, U)>
    where
        T: FromStr + Copy,
        T::Err: Debug + Error + 'static,
        U: FromStr + Copy,
        U::Err: Debug + Error + 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let (a, b) = {
            let params = self.buffer.trim().split_whitespace().collect::<Vec<_>>();
            let a = params[0].parse()?;
            let b = params[1].parse()?;
            (a, b)
        };
        self.buffer.clear();
        Ok((a, b))
    }
    pub fn read_three<T, U, V>(&mut self) -> BoxResult<(T, U, V)>
    where
        T: FromStr + Copy,
        T::Err: Debug + Error + 'static,
        U: FromStr + Copy,
        U::Err: Debug + Error + 'static,
        V: FromStr + Copy,
        V::Err: Debug + Error + 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let (a, b, c) = {
            let params = self.buffer.trim().split_whitespace().collect::<Vec<_>>();
            let a = params[0].parse()?;
            let b = params[1].parse()?;
            let c = params[2].parse()?;
            (a, b, c)
        };
        self.buffer.clear();
        Ok((a, b, c))
    }
    pub fn read_four<T, U, V, W>(&mut self) -> BoxResult<(T, U, V, W)>
    where
        T: FromStr + Copy,
        T::Err: Debug + Error + 'static,
        U: FromStr + Copy,
        U::Err: Debug + Error + 'static,
        V: FromStr + Copy,
        V::Err: Debug + Error + 'static,
        W: FromStr + Copy,
        W::Err: Debug + Error + 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let (a, b, c, d) = {
            let params = self.buffer.trim().split_whitespace().collect::<Vec<_>>();
            let a = params[0].parse()?;
            let b = params[1].parse()?;
            let c = params[2].parse()?;
            let d = params[3].parse()?;
            (a, b, c, d)
        };
        self.buffer.clear();
        Ok((a, b, c, d))
    }
    pub fn read_vector<T>(&mut self) -> BoxResult<Vec<T>>
    where
        T: FromStr + Copy,
        T::Err: Debug + Error + 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed_vec = self
            .buffer
            .trim()
            .split_whitespace()
            .map(|s| s.parse())
            .collect::<Result<Vec<_>, _>>()?;
        self.buffer.clear();
        Ok(parsed_vec)
    }
    pub fn read_matrix<T>(&mut self, lines: u64) -> BoxResult<Vec<Vec<T>>>
    where
        T: FromStr + Copy,
        T::Err: Debug + Error + 'static,
    {
        let mut parsed_matrix = vec![];
        for _ in 0..lines {
            self.reader.read_line(&mut self.buffer)?;
            parsed_matrix.push(
                self.buffer
                    .trim()
                    .split_whitespace()
                    .map(|s| s.parse())
                    .collect::<Result<Vec<_>, _>>()?,
            );
            self.buffer.clear();
        }
        Ok(parsed_matrix)
    }
    pub fn read_chars(&mut self) -> BoxResult<Vec<char>> {
        self.reader.read_line(&mut self.buffer)?;
        let chars = self.buffer.trim().chars().collect::<Vec<_>>();
        self.buffer.clear();
        Ok(chars)
    }
}