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;

namespace ConsoleApp1
{
	class Program
	{
		static void Main(string[] args)
		{
			var input = long.Parse(Console.ReadLine());

			long count = 1;
			foreach(var i in getMinimumDigitIs9(input))
			{
				Console.WriteLine(i);
				count++;
			}
		}

		private static IEnumerable<long> getMinimumDigitIs9(long count)
		{
			long current = 1;
			int sub = 0;
			long tasukazu = 10;
			for (long i = 0; i < count; i++)
			{
				yield return current;
				if (i < 8)
				{
					current++;
				}
				else
				{
					current += tasukazu;
					sub++;
					if (sub == 9)
					{
						tasukazu *= 10;
						sub = 0;
					}
				}
			}
		}
	}
}