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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import math

n, k = map(int, input().split())
a = list(map(int, input().split()))

hq = []

def is_ok(checking):
    cost = 0
    for i in range(n):
        cost += math.ceil(a[i]/checking)-1
    if cost <= k:
        return True
    else:
        return False

def meguru_bisect(ng, ok):
    while (abs(ok-ng)>1):
        mid = (ok+ng)//2
        if is_ok(mid):
            ok = mid
        else:
            ng = mid
    return ok

ok = meguru_bisect(1, int(1e+10)) 
print(int(ok))
# 初期値の範囲は取りえる値-1～+1とする←範囲内はok,ngどちらもあり得るため