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
// D
fscanf(STDIN, '%d', $k);
for ($i = 1; $i < 10; $i++) $sunuke[] = $i;
for ($i = 0, $n = 19; $i < $k; $i++, $n += 10) {
    if (f($n) <= f($n + 1)) $sunuke[] = $n;
}
echo implode(PHP_EOL, array_slice($sunuke, 0, $k));

function f($n)
{
    return $n / array_sum(str_split(strval($n)));
}