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: Wrong Answer)

import math
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 = []
ans = 0
for k in range(N):
  length.append([A[k] / (cut[k]+1), k])

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

C = sum(cut)
res = K - C
if res > 0:
  cut[length[0][1]] += 1
  length[0][0] = length[0][0]*cut[length[0][1]]/(cut[length[0][1]]+1)
new = [length[0]]
k = 1

if res == 1:
  print(math.ceil(max(length[0][0], length[1][0])))
  exit()
while k <res:
  if new[0][0] >= length[k][0]:
    cut[new[0][1]] += 1
    new[0][0] = new[0][0]*cut[new[0][1]]/(cut[[new][1]]+1)
    if len(new) > 1:
      new[0][0] < new[1][0]
      new.sort(key = lambda x: x[0], reverse=True)
    res -= 1
  else: 
    cut[length[k][1]] += 1
    length[k][0] = length[k][0]*cut[length[k][1]]/(cut[length[k][1]]+1)
    new.append(length[k])
    new.sort(key = lambda x: x[0], reverse=True)
    k += 1

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

print(math.ceil(new[0][0]))