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.*;
 
public class Main {
	static Scanner scanner = new Scanner(System.in);
 
	public static void main(String[]$) {
		long k = scanner.nextLong();
		long ans = 0;
		long add = 1;
		for (int i = 0; i < k; i++) {
			long next = ans + add * 10;
			ans += add;
			if (ans * sum(next) > next * sum(ans)) {
				ans = next;
				add *= 10;
			}
			System.out.println(ans);
		}
	}

	static int sum(long n) {
		int sum = 0;
		while (n != 0) {
			sum += n % 10;
			n /= 10;
		}
		return sum;
	}
}