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.Text;
using System.Collections.Generic;
using System.Collections;
using static System.Math;
using System.Linq;
using static System.Array;

namespace ConsoleApp2
{
    class Program
    {
        static long N;
        static long K;
        static long[] A;
        static void Main(string[] args)
        {
            var NK = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            N = NK[0];
            K = NK[1];
            A = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            double L = 0;
            double R = A.Max();

            while (0.000001 < R - L)
            {
                double mid = (R + L) / 2;
                if (check(mid))
                {
                    R = mid;
                }
                else
                {
                    L = mid;
                }
            }

            Console.WriteLine(Ceiling(L));
        }

        static bool check(double mid)
        {
            long ans = 0;
            for (int i = 0; i < N; i++)
            {
                ans += (long)(A[i] / mid);
            }

            return ans <= K;
        }
    }


}