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 Program {
    static void Main (string[] args) {
        long NN = long.Parse (Console.ReadLine ());

        long dig = 1;
        long output = 1;


        for (long i = 0; i < NN ; i++) { //10^10超えてからが本番
            long s = sn(output);//
            if (s*dig < output){
                output += 9 * dig;
                dig*=10;
                i--;
            }else{
                Console.WriteLine (output);
                output += dig;
            }
        }
    }

    static long sn(long NN) {
        long s = 0;
        double f = Math.Log10(((double)NN) ) + 1;
        for (int i = 0; i < f; i++) {
            s += NN % 10;
            NN /= 10;
        }
        return s;
    }
}