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;
class Program
{
	static void Main(string[] args)
	{
		string str = Console.ReadLine();
		long K = long.Parse(str);
		long a = 0;
		long b = 1;
		long c = 0;
		long ba = 0;
		long aa = 1;
		long an = 1;
		long ana = 0;
		long an2 = 0;
		while(c<K){
			for(var h=0;h<9;h++){
			for(var i=1;i<=ba;i++){
				a += b/(long)Math.Pow(10,i);
				an2 = 0;
				for(var j=0;j<=16;j++){
					an2 += (a)/(long)Math.Pow(10,j)%10;
				}
				if(a*an <= ana*an2){
					Console.WriteLine(a);
					c += 1;
				}
			}
			}
			a += 1;
			Console.WriteLine(a);
			if(a>=b*9){
				b *= 10;
				ba += 1;
			}
			an = 0;
			for(var j=0;j<=16;j++){
				an += (a+b)/(long)Math.Pow(10,j)%10;
			}
			ana = (a+b);
			c += 1;
		}
	}
}