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: Wrong Answer)

using System;
using static System.Console;

namespace abc174
{
    class Program
    {
        static int[] ReadNumList()
        {
            var line = ReadLine().Split(' ');
            if (line.Length == 1 && string.IsNullOrEmpty(line[0]))
            {
                return new int[0];
            }
            var numList = new int[line.Length];
            for (var i = 0; i < line.Length; ++i)
            {
                numList[i] = int.Parse(line[i]);
            }
            return numList;
        }
        static void Main()
        {
            var nk = ReadLine().Split(' ');
            var n = int.Parse(nk[0]);
            var k = int.Parse(nk[1]);
            var aList = ReadNumList();

            var startLen = 0;
            var startCut = 0L;
            var endLen = 1;
            var endCut = 0L;
            foreach (var a in aList)
            {
                startLen = Math.Max(startLen, a);
                endCut += a - 1;
            }
            WriteLine(DivSearch(k, startLen, startCut, endLen, endCut, aList));
        }
        static long CalcCutCount(int length, int[] aList)
        {
            var total = 0L;
            foreach (var a in aList)
            {
                total += (long)Math.Ceiling((double)a / length) - 1;
            }
            return total;
        }
        static long DivSearch(int targetCut, int startLen, long startCut, int endLen, long endCut, int[] aList)
        {
            if (startLen - endLen <= 1)
            {
                if (targetCut >= endCut)
                {
                    return endLen;
                }
                else
                {
                    return startLen;
                }
            }
            var centerLen = (startLen + endLen) / 2;
            var centerCut = CalcCutCount(centerLen, aList);
            if (centerCut < targetCut)
            {
                return DivSearch(targetCut, centerLen, centerCut, endLen, endCut, aList);
            }
            else
            {
                return DivSearch(targetCut, startLen, startCut, centerLen, centerCut, aList);
            }
        }
    }
}