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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;


public class D
{
	public static void Main()
	{
		long K = GetLong();
		var sb = new StringBuilder();
		long snuke = 0;
		for(int i = 0; i < K; i++)
		{
			snuke = f(snuke + 1);
			sb.AppendFormat($"{snuke}\n");
		}
		Console.Write(sb);
	}

	private static long f(long x)
	{
		long ans = x;
		double min = ((double)x) / ((double)S(x));
		long div = 1;
		for(int i = 0; i < 16; i++)
		{
			long upper = (x / (div * 10)) * (div * 10);
			long num = (x / div) % 10;
			for(long j = num + 1; j <= 9; j++)
			{
				long y = upper + (num * div) + div - 1;
				double tmp = ((double)y) / ((double)S(y));
				if(tmp < min)
				{
					min = tmp;
					ans = y;
				}
			}
			div *= 10;
		}
		return ans;
	}

	private static long S(long x)
	{
		long ans = 0;
		while(x > 0)
		{
			ans += x % 10;
			x /= 10;
		}
		return ans;
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt(){ return int.Parse(getArg()); }
	public static long GetLong(){ return long.Parse(getArg()); }
	public static double GetDouble(){ return double.Parse(getArg()); }
	public static string GetString(){ return getArg(); }
}