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.Linq;
using System.Collections.Generic;

namespace AtCoder
{
	class Programs
	{
		static void Main ()
		{
			int k = int.Parse (Console.ReadLine ());
			long Base = 1;
			long n = 2;
			while (k > 0) {
				Console.WriteLine (n * Base - 1);
				k--;
				n++;
				if (n % 10 == 0) {
					double L = 0;
					foreach (char c in string.Join("",n*Base-1)) {
						L += c - '0';
					}
					if (((n + 10) * Base - 1) / (L + 1) < ((n + 9) * Base - 1) / L || n ==100) {
						Base *= 10;
						n /= 10;
						continue;
					}
				}
			}
		}
	}
}