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: Accepted)

import java.io.FileNotFoundException;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

    public class Main {
        public static void main(String[] args) throws FileNotFoundException {
            new Main().run();
        }

        void run() {
            Scanner sc = new Scanner(System.in);
            long K = sc.nextLong();
            long ans = 0;
            long add = 1;
            PrintWriter pw = new PrintWriter(System.out);
            
            int cnt = 0;
            while (cnt++ < K) {
                if ((ans + add) * S(ans + add * 10) > (ans + add * 10) * S(ans + add))
                    add = add * 10;
                ans += add;
                pw.println(ans);
            }
            pw.close();
        }

        long S(long a) {
            long ret = 0;
            while (a > 0) {
                ret += a % 10;
                a /= 10;
            }
            return ret;
        }

        static void tr(Object... objects) {
            System.out.println(Arrays.deepToString(objects));
        }


}