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: Wrong Answer)

using System;
using System.Linq;

class Test {
	static void Main(string[] args) {
      var inputs = System.Console.ReadLine()
    	.Split(' ')
    	.Select(s => int.Parse(s))
    	.ToArray();
      int N = inputs[0];
      int K = inputs[1];
      var A = System.Console.ReadLine()
    	.Split(' ')
    	.Select(s => Int64.Parse(s))
    	.ToArray();
      int[] cnt = new int[N];
      for(int i = 0; i < N; i++){
        cnt[i] = 0;
      }
      Array.Sort(A);
      Array.Reverse(A);
      int tmp = 0;
      int maxid = 0;
      double max = 0;
      for(int i = 0; i < K; i++){
        max = 0;
        for(int j = 0; j <= tmp; j++){
          if(max < (double)A[j]/(cnt[j]+1)){
            max = (double)A[j]/(cnt[j]+1);
            maxid = j;
          }
        }
        cnt[maxid]++;
        if(maxid==tmp && tmp < N - 1){
          tmp++;
        }
      }
      max = 0;
      for(int j = 0; j < N; j++){
        if(max < (double)A[j]/(cnt[j]+1)){
          max = (double)A[j]/(cnt[j]+1);
        }
      }
      Console.WriteLine((int)(max+1));
	}
}