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# (Mono-mcs 6.8.0.105) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
class e{
    public static void Main(){
        string[] strs = Console.ReadLine().Split(' ');
        int n = int.Parse(strs[0]);
        int k = int.Parse(strs[1]);
        string[] str = Console.ReadLine().Split(' ');
        List<double> list = new List<double>();
        List<double> cut = new List<double>();
        List<int> counter = new List<int>();
        for(int i=0; i<n; i++){
            double number = double.Parse(str[i]);
            int pos = BinSearch(0, list.Count, cut, number);
            list.Insert(pos, number);
            cut.Insert(pos, number);
            counter.Insert(pos, 1);
        }
        for(int i=0; i<k; i++){
            int size = list.Count-1;
            double num = cut[size];
            int count = counter[size];
            double dflt = list[size];
            count++;
            cut.RemoveAt(size);
            counter.RemoveAt(size);
            list.RemoveAt(size);
            int p = BinSearch(0, list.Count, cut, dflt/count);
            cut.Insert(p, dflt/count);
            list.Insert(p, dflt);
            counter.Insert(p, count);
        }
        double ans = cut[cut.Count-1];
        Console.WriteLine(Math.Ceiling(ans));
    }
    public static int BinSearch(int left, int right, List<double> arr, double n){
        while(left < right){
            int mid = (left+right)/2;
            if(arr[mid] <= n){
                left = mid+1;
            }
            else{
                right = mid;
            }
        }
        return left;
    }
}