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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

main :: IO()
main = do
  k <- readLn :: IO Int
--  putStr . unlines $ take k [show n | n <- [1..], snk n]
--  putStr . unlines $ take k [show (n `div` (f (show n) 0)) | n <- [1..]]
  putStr . unlines $ take k [solve n | n <- [0..]]

solve n = (show (s + 1)) ++ replicate d '9'
  where
    d = div n 9
    s = mod n 9

snk :: Int -> Bool
--snk k = last (show k) == '9' || k < 10
snk k = solve (drop 1 (show k)) || k < 10
  where
    solve :: String -> Bool
    solve "" = True
    solve (s:ss) = s == '9' && solve ss

f :: String -> Int -> Int
f [] n = n
f (s:ss) n = f ss (read [s] + n)