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)

use proconio::*;

fn check(l: usize, k: usize, a: &Vec<usize>) -> bool {
    let mut cnt = 0;
    for &i in a.iter() {
        cnt += (i-1) / l;
    }

    cnt <= k
}

/*

15 5 3
16 5 4

*/

fn main() {
    input!{
        n: usize,
        k: usize,
        a: [usize; n],
    }

    if k == 0 {
        let mut ans = *a.iter().max().unwrap();
        println!("{}", ans);
        return;
    }

    let mut l = 0usize;
    let mut r = *a.iter().max().unwrap();

    while r-l > 1 {
        let mid = (l+r)/2;
        if check(mid, k, &a) {
            r = mid;
        } else {
            l = mid;
        }
    }

    println!("{}", r);
}