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.Collections.Generic;
using System.Linq;
using System.IO;
//using System.Text;
//using System.Text.RegularExpressions;
//using System.Globalization;
//using System.Diagnostics;
using static System.Console;
//using System.Numerics;
//using static System.Math;
using pair = Pair<double, long>;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;
    void chmax<T>(ref T a, T b) where T : IComparable<T> { a = a.CompareTo(b) < 0 ? b : a; }
    void chmin<T>(ref T a, T b) where T : IComparable<T> { a = a.CompareTo(b) < 0 ? a : b; }

    void solve()
    {
        //int N = cin.nextint;

        //double max = int.MaxValue;
        //for (int i = N; i > 0; i--)
        //{
        //    int j = i;
        //    int t = 0;
        //    while (j > 0)
        //    {
        //        t += j % 10;
        //        j /= 10;
        //    }
        //    var d = (double)i / t;
        //    if(d < max)
        //    {
        //        WriteLine(i);
        //        max = d;
        //    }
        //}

        var Q = new PriorityQueue<pair>();
        var K = cin.nextlong;

        //9の個数
        long mol = 1;
        for (int i = 0; i <= 15; i++)
        {
            for (int j = 2; j <= 100; j++)
            {
                long X = j * mol - 1;
                long Y = X;
                long S = 0;
                while (Y > 0)
                {
                    S += Y % 10;
                    Y /= 10;
                }
                Q.Enqueue(new pair(-(double)X / S, -X));
            }
            mol *= 10;
        }

        long id = 0;
        long cnt = 0;
        while(cnt < K)
        {
            var p = Q.Dequeue();
            if (id < -p.s)
            {
                WriteLine(-p.s);
                id = -p.s;
                cnt++;
            }
        }
    }

}


class Pair<T, U> : IComparable<Pair<T, U>> where T : IComparable<T> where U : IComparable<U>
{
    public T f;
    public U s;
    public Pair(T f, U s)
    {
        this.f = f;
        this.s = s;
    }
    public int CompareTo(Pair<T, U> a)
    {
        return f.CompareTo(a.f) != 0 ? f.CompareTo(a.f) : s.CompareTo(a.s);
    }
    public override string ToString()
    {
        return f + " " + s;
    }
}

class PriorityQueue<T> where T : IComparable<T>
{
    List<T> heap; int size;
    int Compare(T x, T y) { return y.CompareTo(x); }
    public PriorityQueue() { heap = new List<T>(); }
    public void Enqueue(T x)
    {
        heap.Add(x);
        int i = size++;
        while (i > 0)
        {
            int p = (i - 1) >> 1;
            if (Compare(heap[p], x) <= 0) break;
            heap[i] = heap[p]; i = p;
        }
        heap[i] = x;
    }
    public T Dequeue()
    {
        T ret = heap[0]; T x = heap[--size];
        int i = 0;
        while ((i << 1) + 1 < size)
        {
            int a = (i << 1) + 1; int b = (i << 1) + 2;
            if (b < size && Compare(heap[b], heap[a]) < 0) a = b;
            if (Compare(heap[a], x) >= 0) break;
            heap[i] = heap[a]; i = a;
        }
        heap[i] = x; heap.RemoveAt(size);
        return ret;
    }
    public int Count { get { return size; } }
    public bool Any() { return size > 0; }
    public T Peek() { return heap[0]; }
}
class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan { get { return ReadLine().Split(); } }
    public int[] scanint { get { return Array.ConvertAll(scan, int.Parse); } }
    public long[] scanlong { get { return Array.ConvertAll(scan, long.Parse); } }
    public double[] scandouble { get { return Array.ConvertAll(scan, double.Parse); } }
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint { get { return int.Parse(next); } }
    public long nextlong { get { return long.Parse(next); } }
    public double nextdouble { get { return double.Parse(next); } }
}