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: Runtime Error)

#![allow(unused_imports)]
#![allow(dead_code)]

use proconio::input;
use proconio::marker::{Bytes, Chars};
use std::collections::*;

fn main() {
    input! {
        n:usize,
        k:i32,
        a:[i32;n],
    }
    let &a_max = a.iter().max().unwrap();
    let ans = meguru_binary_search(
        a_max,
        0,
        |mid| {
            let num = a
                .iter()
                .fold(0, |acc, &a_val| acc + (a_val + mid - 1) / mid - 1);
            num <= k
        },
        1,
    );
    println!("{}", ans);
}

pub fn meguru_binary_search<T, F>(ok: T, no: T, is_valid: F, error: T) -> T
where
    T: num::PrimInt,
    F: Fn(T) -> bool,
{
    itertools::iterate((ok, no), |&(temp_ok, temp_no)| {
        let mid = (temp_ok + temp_no) / T::from(2).unwrap();
        if is_valid(mid) {
            (mid, temp_no)
        } else {
            (temp_ok, mid)
        }
    })
    .find(|&(temp_ok, temp_no)| temp_ok + error >= temp_no && temp_no + error >= temp_ok)
    .unwrap()
    .0
}
pub trait LowerUpperBound<T: Ord> {
    fn lower_bound(&self, value: &T) -> usize;
    fn upper_bound(&self, value: &T) -> usize;
}
impl<T> LowerUpperBound<T> for [T]
where
    T: Ord,
{
    fn lower_bound(&self, value: &T) -> usize {
        meguru_binary_search(self.len() as i64, -1, |x| self[x as usize] >= *value, 1) as usize
    }
    fn upper_bound(&self, value: &T) -> usize {
        meguru_binary_search(self.len() as i64, -1, |x| self[x as usize] > *value, 1) as usize
    }
}