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 bla
{
    class Program
    {
        static void Main(string[] args)
        {
            int k = int.Parse(Console.ReadLine());
            int first = 1;
            string nines = "";
            for (int i = 0; i < k; i++)
            {
                Console.WriteLine(first + nines);
                if (first == 9)
                {
                    first = 1;
                    nines += "9";
                }
                else
                {
                    first++;
                }
            }
        }
    }
}