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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
$k = (int)trim(fgets(STDIN));

if ($k < 10) {
    for ($i = 1; $i <= $k; $i++) {
        echo $i . PHP_EOL;
    }
    exit();
} else {
    for ($i = 1; $i <= 9; $i++) {
        echo $i . PHP_EOL;
    }

    $t = 1;
    $iii = 1;
    for ($i = $i; $i <= $k; $i++) {
        $s = '';
        for ($j = 0; $j < $t; $j++) {
            $s .= '9';
        }

        echo $iii . $s . PHP_EOL;

        if ($iii % 9 === 0) {
            $t++;
            $iii = 1;
        } else {
            $iii++;
        }
    }
}