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;
using System.Collections.Generic;
using System.Linq;
class Program
{
    static void Main(string[] args)
    {
        var K = int.Parse(Console.ReadLine());
        List<long> list = new List<long>();
        var first = new long[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
        list.AddRange(first);
        var keta = 1;
        var top = 0;
        while(list.Count < K)
        {
            if (top == 9)
            {
                top = 1;
                keta++;
            }
            else
            {
                top++;
            }
            long n = (long)Math.Pow(10, keta);
            double prev = 9999999999999;
            List<long> tmp = new List<long>();
            for (int i = 1; i < keta+1; i++)
            {
                var current = top*n + (long)Math.Pow(10, i) - 1;
                double val = 1.0*current/(double)CalcDigitSum(current);
                if (val < prev)
                {
                    tmp.Clear();
                }
                tmp.Add(current);
                prev = val;
            }
            list.AddRange(tmp);
        }
        Console.WriteLine(string.Join("\n", list.Take(K)));
    }
    static long CalcDigitSum(long N)
    {
        long n = N;
        long sum = 0;
        while (n >= 10)
        {
            var r = n % 10;
            sum += r;
            n /= 10;
        }
        return sum + n;
    }
}