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: Time Limit Exceeded)

import java.util.Scanner;
import java.util.List;
import java.util.ArrayList;

public class Main {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		long K = scanner.nextInt();
		long resultLong=0; 
		long number = 0;
		while(resultLong<K) {
			number++;
			String s = number+"";
			long N=0;
			for(int i=0; i<s.length(); i++) {
				N = N + Integer.parseInt(s.charAt(i)+"");
			}
			if(number/N<=1) {
				System.out.println(number);
				resultLong++;
			}
		}

	}
}