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: Runtime Error)

import math
n,k = map(int,input().split())
alist = list(map(int,input().split()))

max = 0
for i in range(n):
    if max < alist[i]:
        max = alist[i]

max_length = max

cur_length = max_length//2

cuts = 0
for i in range(n):
    cuts += math.ceil(alist[i]/cur_length)-1

test_k = cuts
prev_length = 0
while(cur_length != prev_length):

    prev_length = cur_length
    cuts = 0
    if test_k <= k:
        max_length = cur_length
        cur_length = cur_length//2
        for i in range(n):
            cuts += math.ceil(alist[i]/cur_length)-1
    else:
        cur_length = (cur_length+max_length)//2
        for i in range(n):
            cuts += math.ceil(alist[i]/cur_length)-1
    test_k = cuts

if test_k > k:
    print(cur_length+1)
else:
    print(cur_length)