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 Ruby (2.7.1) (judge verdict: Accepted)

def max(a, b); a < b ? b : a; end
def min(a, b); a < b ? a : b; end
def divceil(a, b); (a + b - 1) / b; end

class Problem
  attr_accessor *(?a..?z).to_a.map(&:to_sym)

  def initialize
    @n,@k = gets.to_s.split.map{ |v| v.to_i }
    @a = gets.to_s.split.map{ |v| v.to_i }
  end

  def solve
    lo = 0
    hi = 10**10
    (lo..hi).bsearch do |x|
      query(x)
    end
  end

  def query(x)
    cutnum(x) <= k
  end

  def cutnum(x)
    a.map{ x == 0 ? _1 + 1 : divceil(_1, x) - 1 }.sum
  end

  def show(ans)
    puts ans == 0 ? 1 : ans
  end
end

Problem.new.instance_eval do
  show(solve)
end