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: Runtime Error)

#!/usr/bin/env pypy3

import math

def num_cuts(A, ml):
	ret = 0
	for a in A:
		ret += (math.ceil(a / ml) - 1)
	return ret

def ok(A, ml):
	return num_cuts(A, ml) <= K

def ans(A, K):

	low = 0.5
	high = max(A)+1

	assert(not(ok(A, low)))
	assert(ok(A, high))

	while (high - low) > 0.1:
		mid = (low + high) / 2
		if ok(A, mid):
			high = mid
		else:
			low = mid

	low = max(1, math.floor(low) - 5)

	for i in range(100):
		p = low + i/3
		q = low + (i+1) / 3

		if not(ok(A, p)) and ok(A, q):
			return math.ceil(q)


N, K = input().split()
N = int(N)
K = int(K)

A = list(map(int, input().split()))

print(ans(A, K))