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: Accepted)

import math
import sys
from itertools import permutations
input = sys.stdin.readline

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

fin = 1000000000000
def check(x):
	global arr, n, k, fin
	# print("x",x)
	cur=0
	for i in range(n):
		cur+=(math.ceil(arr[i]/x)-1)
		# print(cur)
		if cur>k:
			return False
	
	return True

def bs(l, r):
	global arr, n, k, fin
	if r>=l:
		mid = l+(r-l)//2
		if check(mid):
			fin = min(fin, mid)
			bs(l, mid-1)
		else:
			bs(mid+1, r)

if k==0:
	print(max(arr))
else:
	bs(1, max(arr))
	print(fin)