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 Go (1.6) (judge verdict: Wrong Answer)

package main
import (
  "container/list"
  "fmt"
  "os"
  "strconv"
)
func main() {
  var k int64
  var m int64 = 0
  fmt.Scan(&k)
  if k < 9 {
    for i:=int64(0);i<k;i++ {
      m++
      fmt.Println(m)
    }
    os.Exit(0)
  }
  for i:=int64(0);i<8;i++ {
    m++
    fmt.Println(m)
  }
  queue := list.New()
  queue.PushBack("9")
  for i:=int64(8);i<k;i++ {
    s,_ := queue.Remove(queue.Front()).(string)
    fmt.Println(s)
    for j:=1;j<10;j++ {
      queue.PushBack(strconv.Itoa(j)+s)
    }
  }
}