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)

class BinarySearch
  def initialize(t, &b)
    @t = t
    @b = b
  end
  def search(f, t, isMin)
    return isMin ? t : f if f-t == 1
    m = (f+t)/2
    n = @b.call(m)
    if n > @t || (n==@t && isMin) then
      search(f, m, isMin)
    else
      search(m, t, isMin)
    end
  end
end

N, K = gets.chomp.split(" ").map(&:to_i)
A = gets.chomp.split(" ").map(&:to_i)

(puts A.max; exit) if K == 0
(puts 1; exit) if K >= A.inject(:+) - N

bs = BinarySearch.new(K){|x|
  A.inject(0){|r, a|
    r + (a+x-1)/x - 1
  }
}

puts bs.search(A.max, 1, false)