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.Scanner;

/**
 *
 */
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int K = sc.nextInt();

        long[] ans = solve(K);
        for (int i=0; i<ans.length-1; i++) {
            System.out.println(ans[i]);
        }
    }

    private static long[] solve(int K) {
        long[] ans = new long[K+1];
        int digit = 1;

        ans[0] = 1;
        for (int i=1; i<K; i++) {
            ans[i] += ans[i-1] + (long)Math.pow(10, digit-1);

            if ((i+1)%9 == 0) {
                digit++;
            }
        }

        return ans;
    }
}