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 PHP (7.4.4) (judge verdict: Accepted)

<?php
  list($n, $k) = explode(" ", trim(fgets(STDIN)));

  $a = array_map('intval', explode(" ", trim(fgets(STDIN))));

  sort($a);

  $R = $a[$n-1];
  $L = 0;

  while($R-$L>1){
    $ans = intdiv($R+$L, 2);
    //echo "RL:".$R." ".$L." ".$ans.PHP_EOL;
    $cut = 0;
    for ($i=0; $i<$n; $i++) {
      $cnt = intdiv($ans + $a[$i]-1, $ans)-1;
      if($cnt > 0){
        $cut += $cnt;
      }
    }
    //echo $cut.PHP_EOL;
  
    if($cut <= $k){
      $R = $ans;
    }else{
      $L = $ans;
    }
    
  }

  echo $R;