Problem:
Score : 500 points

Problem Statement

Let S(n) denote the sum of the digits in the decimal notation of n.
For example, S(123) = 1 + 2 + 3 = 6.

We will call an integer n a Snuke number when, for all positive integers m such that m > n, \frac{n}{S(n)} \leq \frac{m}{S(m)} holds.

Given an integer K, list the K smallest Snuke numbers.

Constraints

1 \leq K

The K-th smallest Snuke number is not greater than 10^{15}.

Input

Input is given from Standard Input in the following format:

K

Output

Print K lines. The i-th line should contain the i-th smallest Snuke number.

Sample Input 1

10

Sample Output 1

1
2
3
4
5
6
7
8
9
19

Solution in Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

use List::Util qw/sum/;
my $k = <>; chomp $k;
$sunuke = 1;

$count = 0;
$n=1;
while ($count < $k) {
    my @digit = split //, $n;
    my $s = $n / sum @digit;

    if ($sunuke <= $s) {
        my @next_digit = split //, $n+1;
        my $next_s = ($n+1) / sum @next_digit;

        if ($s <= $next_s) {
            print "$n\n";
            $count++;
            $sunuke = $s;
        }
    }
    $n++;
}