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: Time Limit Exceeded)

import java.io.*;
import java.util.*;

class Main
{
    public static void main(String args[])throws Exception
    {
        BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
        String s[]=bu.readLine().split(" ");
        int n=Integer.parseInt(s[0]),k=Integer.parseInt(s[1]),i,a[]=new int[n],ans=1;
        s=bu.readLine().split(" ");
        for(i=0;i<n;i++)
        a[i]=Integer.parseInt(s[i]);
        int l=1,r=1000000000,mid;
        while(l<=r)
        {
            mid=(l+r)/2;
            int cn=cuts(a,mid);
            if(cn>k) l=mid+1;
            else {ans=mid; r=mid-1;}
        }
        System.out.print(ans);
    }

    static int cuts(int a[],int k)
    {
        int i,c=0;
        for(i=0;i<a.length;i++)
        {
            int cur=a[i];
            while(cur>k)
            {
                cur-=k;
                c++;
            }
        }
        return c;
    }
}