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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
	
	public static void main(String[] args)
	{
		Scanner s=new Scanner(System.in);
		
		int n=s.nextInt();
		double k=s.nextInt();
		
		double[] arr=new double[n];
		
		double max=0;
		
		for(int i=0;i<n;i++)
		{
			arr[i]=s.nextInt();
			
			max=Math.max(max,arr[i]);
		}
		
		long start=0;
		long end=1000000001;
		
		double ans=max;
		
		while(start<=end)
		{
			long mid=(start+end)/2;
			
			double count=0;
			
			for(int i=0;i<n;i++)
			{
				if(arr[i]>mid)
				count=count+Math.floor(arr[i]/mid);
			}
			
			if(count<=k)
			{
				ans=mid;
				end=mid-1;
			}
			else
			{
				start=mid+1;
			}
			
		}
		
		System.out.println((long)Math.min(ans,max));
		
	}
	
}