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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int k = sc.nextInt();
        sc.close();

        ArrayList<Long> ll = new ArrayList<Long>();
        ArrayList<Double> dl = new ArrayList<Double>();
        ll.add(1L);
        dl.add(1.0);

        for (int i = 2; i < 102; i++) {
            int s = 0;
            int ti = i;
            for (int j = 0; j < 8; j++) {
                int div = (int) (Math.pow(10, 7 - j));
                if (ti >= div) {
                    int ts = ti / div;
                    s += ts;
                    ti -= ts * div;
                }
            }
            double f = (double) i / (double) s;
            // System.out.println(f + " " + i + " " + s);
            while (dl.get(dl.size() - 1) > f) {
                ll.remove(ll.size() - 1);
                dl.remove(dl.size() - 1);
            }
            ll.add((long) i);
            dl.add(f);
        }

        long nine = 0;
        int count = 0;
        for (int i = 0; i < 1; i++) {
            nine += (long) (Math.pow(10, count)) * 9;
            nine += (long) (Math.pow(10, count + 1)) * 9;
            count += 2;
            for (int j = 1; j <= 99; j++) {
                long tl = nine + j * (long) (Math.pow(10, count));
                long stl = tl;
                long s = 0;
                for (int m = 0; m < 17; m++) {
                    long div = (long) (Math.pow(10, 16 - m));
                    if (tl >= div) {
                        long ts = tl / div;
                        s += ts;
                        tl -= ts * div;
                    }
                }
                double f = (double) stl / (double) s;
                // System.out.println(f + " " + i + " " + s);
                while (dl.get(dl.size() - 1) > f) {
                    ll.remove(ll.size() - 1);
                    dl.remove(dl.size() - 1);
                }
                ll.add(stl);
                dl.add(f);
                // System.out.println(stl + " " + f);
            }
        }

        nine = 0;
        count = 0;
        for (int i = 0; i < 3; i++) {
            nine += (long) (Math.pow(10, count)) * 9;
            nine += (long) (Math.pow(10, count + 1)) * 9;
            nine += (long) (Math.pow(10, count + 2)) * 9;
            nine += (long) (Math.pow(10, count + 3)) * 9;
            count += 4;
            for (int j = 1; j <= 9999; j++) {
                long tl = nine + j * (long) (Math.pow(10, count));
                long stl = tl;
                long s = 0;
                for (int m = 0; m < 17; m++) {
                    long div = (long) (Math.pow(10, 16 - m));
                    if (tl >= div) {
                        long ts = tl / div;
                        s += ts;
                        tl -= ts * div;
                    }
                }
                double f = (double) stl / (double) s;
                // System.out.println(f + " " + i + " " + s);
                while (dl.get(dl.size() - 1) > f) {
                    ll.remove(ll.size() - 1);
                    dl.remove(dl.size() - 1);
                }
                ll.add(stl);
                dl.add(f);
                // System.out.println(stl + " " + f);
            }
        }

        for (int i = 0; i < ll.size(); i++) {
            System.out.println(ll.get(i));
        }
    }
}