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.util.Scanner;

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

		for (int i=1; i<=9&&k>0; i++){
			System.out.println(i);
			k--;
		}
		for (int i=1; i<=9&&k>0; i++){
			System.out.println(i*10+9);
			k--;
		}
		for (int e=2; e<=10&&k>0; e++){
			long a = (long)Math.pow(10, e);
			for (int i=e-1; i<=10*e-1&&k>0; i++){
				System.out.println((i+1)*a-1);
				k--;
			}
		}
		for (int i=11-1; i<=10*(11-1)-1&&k>0; i++){
			System.out.println((i+1)*(long)Math.pow(10,11)-1);
			k--;
		}
		for (int e=12; k>0; e++){
			long a = (long)Math.pow(10,e);
			for (int i=e-2; i<=10*(e-1)-1&&k>0; i++){
				System.out.println((i+1)*a-1);
				k--;
			}
		}
	}
}