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 Perl (5.26.1) (judge verdict: Wrong Answer)

#!/usr/bin/perl

my ($n,$k) = map { $_ - 0 } split(/\s+/,<STDIN>);
my @aa = map { $_ - 0 } split(/\s+/,<STDIN>);

my @sa = sort { $a <=> $b } @aa;

my $sum1 = 0;
for(my $i=0;$i<$n;$i++){
  $sum1 += $aa[$i];
}

if( $k == 0 ){
  print "$sa[$#sa]\n"; exit(0);
}
if( $k == 1 ){
  my $d2 = int( ($sa[$#sa] + 1)/2 );
  if( $n==1 ){
    print "$d2\n";
  } else {
    $d2 = $sa[0] if $sa[0] > $d2;
    print "$d2\n";
  }
  exit(0);
}

my $mx = 10 ** 9;
my $mn = 1;

my $mx_c = &chk($mx);
my $mn_c = &chk($mn);

#print "mx,mn_c = $mx_c , $mn_c \n";

while( $mx - $mn > 1 ){
  my $md = int( ($mx + $mn)/2 );
  my $md_c = &chk($md);
  if( $md_c <= $k and $k <= $mn_c ){
    $mx = $md;
    $mx_c = $md_c;
  } else { #( $mx_c <= $k < $md_c ){
    $mn = $md;
    $mn_c = $md_c;
  }
  #print "mx,mn_c = $mx_c , $mn_c \n";
}

if( $mn_c == $k ){
  print "$mn\n";
} elsif( $mx_c == $k ){
  print "$mx\n";
} else {
  if( $mx_c < $k and $k < $mn_c ){
    print "$mx\n";
  } elsif( $mn_c < $k ){
    print "$mn\n";
  } else {
    print "$mx\n";
  }
}

exit(0);

sub chk {
  my $v = shift;
  my $s = 0;
  for(my $i=0;$i<$n;$i++){
    my $vv = int((( $v - 1 ) + $aa[$i]) / $v) - 1;
    $s += $vv;
  }
  return $s;
}