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.Linq;

class D
{
	static void Main()
	{
		double m = 1000000000000000, v;
		var q = new int[13].SelectMany((y, d) => new int[1000].Select((z, i) => i + new string('9', d)))
			.Select(long.Parse)
			.Distinct()
			.OrderBy(x => -x)
			.Where(x =>
			{
				var r = (v = (double)x / $"{x}".Sum(c => c - '0')) <= m;
				if (r) m = v;
				return r;
			})
			.Reverse()
			.Take(int.Parse(Console.ReadLine()));
		Console.WriteLine(string.Join("\n", q));
	}
}