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 ());
			if (k <= 9) {
				for (int i = 1; i < k; i++) {
					Console.WriteLine (i);
				}
			} else {
				for (int i = 1; i <= 9; i++) {
					Console.WriteLine (i);
					k--;
				}
				long Base = 10;
				long n = 2;
				while (k > 0) {
					if (n > 20) {
						Base *= 10;
						n = 2;
					}
					Console.WriteLine (n * Base - 1);
					n++;
					k--;
				}
			}
		}
	}
}