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)

use POSIX qw(ceil);
my ($N,$K) =split(/ /,<>);
my $s = <>; chomp $s;
my @dat = split(/ /,$s);

my $ok =10**9;
#$ok =10;
my $ng =1; 

while(){
    if(($ok-$ng)<=1){last;}
    my $cut =int(($ok+$ng)/2);
    my $sum=0;
    for(my $i=0;$i<=$#dat;$i++){
        #print "$dat[$i]\n";
        #$sum = $sum + (int(($cut-0.1+$dat[$i])/$cut)-1);
        $sum = $sum + (ceil($dat[$i]/$cut)-1);
        #print "$dat[$i] $cut $sum\n";
    }
    if($sum <= $K){
        $ok = $cut;
    }else{
        $ng = $cut
    }
    #print "cut $cut $ok $ng\n";
    #last;
}

$ok = ceil($ok);

print "$ok\n";