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;

public class Hello
{
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        var n = int.Parse(line[0]);
        var k = int.Parse(line[1]);
        line = Console.ReadLine().Trim().Split(' ');
        var a = Array.ConvertAll(line, int.Parse);
        getAns(n, k, a);
    }
    static void getAns(int n, int k, int[] a)
    {
        var ok = 1000000000;
        var ng = 0;
        while (ok - ng > 1)
        {
            var mid = ng + (ok - ng) / 2;
            if (CanCut(n, k, a, mid)) ok = mid;
            else ng = mid;
        }
        Console.WriteLine(ok);
    }
    static bool CanCut(int n, int k, int[] a, int t)
    {
        var count = 0;
        for (int i = 0; i < n; i++)
        {
            if (a[i] % t == 0) count += a[i] / t - 1;
            else count += a[i] / t;
            if (count > k) return false;
        }
        return true;
    }
}