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: Wrong Answer)

import java.util.Comparator;
import java.util.Scanner;
import java.util.TreeSet;

public class Main {
    
    private static class Maruta {
        private final double originalLen;
        private int cuts = 0;
        private double len;
        
        private Maruta(int originalLen) {
            this.originalLen = originalLen;
            this.len = originalLen;
        }
        
        public void cut() {
            cuts++;
            len = originalLen / (cuts + 1);
        }
    }
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        
        final int N = sc.nextInt();
        final int K = sc.nextInt();
        final int[] As = new int[N];
        
        TreeSet<Maruta> ms = new TreeSet<>(Comparator.comparing(m -> m.len));
        for (int i = 0; i < N; i++) {
            As[i] = sc.nextInt();
            ms.add(new Maruta(As[i]));
        }
        
        for (int i = 0; i < K; i++) {
            Maruta longest = ms.pollLast();
            longest.cut();
            ms.add(longest);
        }
        
        int result = (int) Math.ceil(ms.last().len);
        System.out.println(result);
    }
}