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 Scala (2.11.7) (judge verdict: Wrong Answer)

object Main {
  def main(args:Array[String]) = {
    val sc = new java.util.Scanner(System.in)
    val k = sc.nextInt

    Stream.from(1).filter(isSunuke).take(k).foreach(println)
  }

  def s(n: Int): Int = n.toString.map(_.toString.toInt).sum
  def isSunuke(n: Int): Boolean = {
    val m0 = if(n % 10 == 9) n + 1 else n
    val m = m0 - (m0 % 10) + 9
    n * s(m) <= m * s(n)
  }
}