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

namespace ABC174
{
    class Program
    {
        static void Main(string[] args)
        {
            var NK = Console.ReadLine().Split().Select(long.Parse).ToArray();
            var N = NK[0]; var K = NK[1];
            var A = Console.ReadLine().Split().Select(long.Parse).OrderBy(x => x).ToArray();
            // var CA = Enumerable.Repeat(0, (int)N).Select(_ => Console.ReadLine().Split().Select(long.Parse).ToArray()).ToArray();
            var ok = A.Max();
            var ng = 0L;

            while (1 < Math.Abs(ok - ng))
            {
                var m = (ok + ng) / 2;
                var cnt = 0L;
                for (int i = 0; i < N; i++)
                {
                    cnt += (long)Math.Ceiling((double)A[i] / (double)m) - 1;
                }

                if (cnt <= K)
                    ok = m;
                else
                    ng = m;

            }
            Console.WriteLine(ok);
        }
    }
}