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.Generic;
using System.Linq;

class D
{
	static void Main() => Console.WriteLine(string.Join("\n", GetNumbers().Take(int.Parse(Console.ReadLine()))));

	static IEnumerable<long> GetNumbers()
	{
		long d10 = 1, t = 0;
		for (int d = 0; ; d++)
		{
			for (int i = 0; ; i += 10)
			{
				var v0 = (i + 1) * d10 - 1;
				if (($"{i}".Sum(c => c - '0') + 9 * d) * d10 < v0) break;
				for (int j = 0; j < 10; j++)
				{
					var v = v0 + j * d10;
					if (v <= t) continue;
					yield return t = v;
				}
			}
			d10 *= 10;
		}
	}
}