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

use proconio::{fastout, input};
use std::cmp::{max, min};

const INF: i32 = 1001001001;
const LNF: i64 = 1001001001001001001;
const MOD: i32 = 1000000007;

#[fastout]
fn main() {
  input! {
    n: usize,
    k: i64,
    a: [i64; n],
  }
  let k = k + n as i64;
  let mut ok: i64 = LNF;
  let mut ng: i64 = 0;
  while (ok - ng).abs() != 1 {
    let x = (ok + ng) >> 1;
    let mut cnt = 0;
    for i in 0..n {
      cnt += (a[i] + x - 1) / x;
    }
    if cnt <= k {
      ok = x;
    } else {
      ng = x;
    }
  }
  println!("{}", ok);
}