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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;

namespace AtCoder.ABC101
{
    class d
    {
        static void Main(string[] args)
        {
            var line = Console.ReadLine().Trim();
            var K = int.Parse(line);
            var cnt = 0;
            var ketaCnt = 0;
            while (true)
            {
                for(var i = 1; i < 10; ++i)
                {
                    if (i == 1 && ketaCnt > 2 || i == 2 && ketaCnt > 3 || i == 3 && ketaCnt > 4
                        || i == 4 && ketaCnt > 5 || i == 5 && ketaCnt >= 7 || i == 6 && ketaCnt >= 8
                        || i == 7 && ketaCnt >= 9 || i == 8 && ketaCnt >= 10 || i == 9 && ketaCnt >= 11)
                    {
                        for (var k = 0; k < 10; ++k)
                        {
                            Console.Write(i);
                            for (var j = 0; j < ketaCnt; ++j)
                            {
                                if (j == 0)
                                {
                                    Console.Write(k);
                                }
                                else
                                {
                                    Console.Write(9);
                                }
                            }
                            Console.WriteLine();
                            ++cnt;
                            if (cnt == K) return;
                        }
                    }
                    else
                    {
                        Console.Write(i);
                        for (var j = 0; j < ketaCnt; ++j)
                        {
                            Console.Write(9);
                        }
                        Console.WriteLine();
                        ++cnt;
                        if (cnt == K) return;
                    }
                }
                ++ketaCnt;
            }
        }
    }
}