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.Scanner;

public class Main {
    public static class Solver {
        int n;
        int k;
        public Solver() {
            Scanner sc = new Scanner(System.in);
            long cnt = 0;
            long k = sc.nextLong();
            long n = 0;
            while (cnt < k) {
                if (cnt < 9) {
                    n++;
                } else {
                    int jmp;
                    jmp = 10;
//                    if (n > 10000000) {
//                        jmp = 1000;
//                    } else if (n > 1000) {
//                        jmp = 100;
//                    } else {
//                        jmp = 10;
//                    }
                    if (n > 1000) {
                        jmp = 100;
                    }
                    n += jmp;

                    while (f(n) > f(n + jmp)) {
                        n += jmp;
                    }
                }
                System.out.println(n);
                cnt++;
            }
        }

        double f (long digit) {
            return digit / (double) S(digit);
        }

        double S(long digit) {
            long cp = digit;
            int sum = 0;
            while (cp >= 10) {
                sum += cp % 10;
                cp /= 10;
            }

            sum += cp;
            return sum;
        }
    }

    public static void main(String[] args) {

        new Solver();
    }
}