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 Julia (1.4.0) (judge verdict: Time Limit Exceeded)

using DataStructures
const double = Float64
const int = Int64

parseint(x) = parse(int, x)
readint() = map(parseint, split(readline()))

function cutN(A,L)
  N = length(A)
  c = 0
  for i in 1:N
    c += A[i]÷L
    if A[i]%L == 0
      c -= 1
    end
  end
  return c
end

function main()
  N,K = readint()
  A = readint()

  LB = 0
  for i in 1:N
    if LB < A[i]
      LB = A[i]
    end
  end
  LA = 1
  #LB = 10^9
  KA = cutN(A,LA)
  KB = cutN(A,LB)

  if KB == K
    println(LB)
    return
  elseif KA == K
    println(LA)
    return
  end

  while true
  LC = (LA + LB)÷2
  KC = cutN(A,LC)
  if KC == K && KC != cutN(A,LC-1)
    println(LC)
    return
  end

  if KC <= K
    LB = LC
  else
    LA = LC
  end

  #println(KA," ", KB," ", KC)
end  



end

main()