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 Python (3.8.2) (judge verdict: Accepted)

import math
from collections import deque
N, K = map(int, input().split())
A = list(map(int, input().split()))
S = sum(A)
cut = []
for k in range(N):
  cut.append(K*A[k]//S)

length = []
for k in range(N):
  length.append([A[k] / (cut[k]+1), k])

length.sort(key = lambda x: x[0], reverse=True)

def nibun_insert(lis, item):
  end = len(lis)
  start = 0
  now = (end+start)//2
  while end > start+1:
    if lis[now][0] > item[0]:
      start = 0 + now
      now = (now + end)//2
    else:
      end = 0 + now
      now = (now + start)//2
  lis.insert(now+1, item)
  return lis

C = sum(cut)
res = K - C
length = length[:res+1]
length = deque(length)
for _ in range(res):
  a = length.popleft()
  cut[a[1]] += 1
  a[0] = a[0]*cut[a[1]]/(cut[a[1]]+1)
  if a[0] <= length[-1][0]:
    continue
  elif a[0] >= length[0][0]:
    length.appendleft(a)
  else:
    length = nibun_insert(length, a)
  length.pop()

print(math.ceil(length.popleft()[0]))