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.Linq;
class Program
{
    static void Main(string[] args)
    {
        var K = int.Parse(Console.ReadLine());
        var first = new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
        if (K <= 9)
        {
            for (int i = 0; i < K; i++)
            {
                Console.WriteLine("{0}\n", first[i]);
            }
        }
        else
        {
            Console.WriteLine(string.Join("\n", first));
            int keta = 1;
            for (int i = 10; i < K; i++)
            {
                if (i % 10 == 9) ++keta;
                var n = Math.Pow(10, keta);
                Console.WriteLine(n * ((i+1)%10) + n -1);
            }
        }
    }
}