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 Scala (2.13.1) (judge verdict: Wrong Answer)

import java.util.Scanner;

object Main extends App {

  val sc = new Scanner(System.in);

  val n = sc.nextInt();
  val k = sc.nextInt();
  val ls = Array.fill(n)(sc.nextInt());

  @scala.annotation.tailrec
  def search(answer1: Int, answer2: Int): Int = {
    if (answer1 + 1 >= answer2) {
      answer2;
    } else {
      val mid = (answer1 + answer2) / 2;
      val c = ls.map { l =>
        (l - 1) / mid;
      }.sum;
      if (c > k) {
        search(mid, answer2);
      } else {
        search(answer1, mid);
      }
    }
  }

  val answer = search(1, ls.max);

  println(answer);
}