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.io.*;
import java.util.*;

public class Main {
	public static void main(String[] args) {
		int k = 0;
		double sk = 0;
		
		try (BufferedReader br = new BufferedReader(new InputStreamReader(System.in))) {
			k = Integer.parseInt(br.readLine());
		} catch (IOException e) {
			return;
		}
		
		for (int m = 1; k > 0; m++) {
			double sm = 0;
			for (int i = m; i > 0; i /= 10) {
				sm += i % 10;
			}
			sm = m / sm;
			
			int m2 = m + 1;
			double sm2 = 0;
			for (int i = m2; i > 0; i /= 10) {
				sm2 += i % 10;
			}
			sm2 = m2 / sm2;
			
			if (sm <= sm2) {
				System.out.println(m);
				k--;
			}
		}
		
	}
}