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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

public static class Solution
{
    static int K;
    static int[] A;

    // [ok,ng) or (ng,ok]
    static int Search(int ok, int ng)
    {
        while (Math.Abs(ok - ng) > 1)
        {
            var mid = (ok + ng) / 2;
            if (Solve(mid))
            {
                ok = mid;
            }
            else
            {
                ng = mid;
            }
        }
        return ok;
    }

    static bool Solve(int max)
    {
        var rem = K;
        foreach (var a in A)
        {
            var div = a / max;
            if (a % max == 0)
            {
                div--;
            }

            rem -= div;
            if (rem < 0)
            {
                return false;
            }
        }
        return true;
    }

    public static void Main()
    {
        var vals = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        var N = vals[0];
        K = vals[1];
        A = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();

        var answer = Search((int)1e9, 0);
        Console.WriteLine(answer);
    }
}