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.*;

public class Main {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int k = scanner.nextInt();
		int digit = 1;
		int count = 10;



		while(k > 0) {		
			int baseNineNum = 0;
			for (int i = 1; i < digit; i++) {
				if (fanc(makeCheckNum(baseNineNum,digit)) > fanc(makeCheckNum(i, digit))) {
					baseNineNum = i;
				}
			}
			count = (int)Math.pow(10 , digit - baseNineNum - 1);
			while(count < (int)Math.pow(10 , digit - baseNineNum)) {
				System.out.println(count + makeNineStr(baseNineNum));
				count++;
				k--;
				if (k <= 0) {
					break;
				}
			}
			digit++;
		}
	}

	public static double fanc(long x) {
		return (double)x/numStrSum(x);
	}

	public static long numStrSum(long x) {
		if (x < 10) {
			return x;
		} else {
			return numStrSum(x/10) + x % 10;
		}
	}

	public static String makeZeroStr(int x) {
		String str = "";
		for (int i = 0 ; i < x; i++) {
			str = str + "0";
		}
		return str;
	}
	public static  String makeNineStr(int x) {
		String str = "";
		for (int i = 0 ; i < x; i++) {
			str = str + "9";
		}
		return str;
	}

	public static long makeCheckNum(int i, int digit) {
		return Long.parseLong("1" + makeZeroStr(digit - i - 1) + makeNineStr(i));
	}
}