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: Runtime Error)

require 'set'; require 'prime'; require 'pp'
INF=Float::INFINITY; MOD=10**9+7
n,k = gets.chomp.split.map(&:to_i)
a = gets.chomp.split.map(&:to_i)
@a = a.sort.reverse
@n = n
@k = k

l = 0
r = 10**9

def ok?(len)
  count = 0
  @n.times do |i|
    break if @a[i] <= len
    count += @a[i] / len - 1
    count += 1 if @a[i] % len != 0
    # p [len, 'ok?', i, @a[i], count]
    return false if count > @k
  end
  true
end

while l < r
  mid = (l + r) / 2
  # p [[l, r], mid, ok?(mid)]
  if ok?(mid)
    r = mid
  else
    l = mid + 1
  end
end

puts l