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 Kotlin (1.3.71) (judge verdict: Accepted)

import kotlin.math.*

fun str() = readLine()!!
fun read(d:String = " ") = str().split(d)
fun <T> list(d:String = " ",f:String.()->T) = read(d).map {f(it)}
fun list() = list {toInt()}

typealias Num = Int

fun binarySearch(ok:Num,ng:Num,eps:Num,f:(Num)->Boolean):Num {
	var _ok = ok
	var _ng = ng
	while(abs(_ok-_ng)>eps) {
		val mid = (_ok+_ng)/2
		if(f(mid))
			_ok = mid
		else
			_ng = mid
	}
	return _ok
}

fun main() {
	val (n,k) = list()
	val a = list()
	println(binarySearch(1000000000,0,1) {l->
		a.map {(it+l-1)/l-1}.sum()<=k
	})
}