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: Time Limit Exceeded)

n,k = gets.chomp.split(" ").map(&:to_i)
a_arr = gets.chomp.split(" ").map(&:to_i)

len_arr = []
a_arr.each do |a|
  # もとの長さ, m等分, m等分したあとの長さ
  len_arr << [a, 1, a]
end

len_arr.sort_by!{|len| -len[-1]}

# でかいものから順に等分することを繰り返す
k.times do
  # もとの長さ, m等分, m等分したあとの長さ
  a, m, l = len_arr.shift
  m += 1
  l = a / m.to_f
  # lの位置を二部探索で求める
  index = len_arr.bsearch_index {|len| l >= len[-1]} || -1
  len_arr.insert(index, [a, m, l])
end

puts len_arr[0][-1].ceil