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: Accepted)

import Data.Ratio
import Data.List

main = do
  k <- readLn :: IO Int

  mapM_ print $ take k $ snuke

  where
    snuke = [1..9] ++ (snuke' 10)
    snuke' :: Integer -> [Integer]
    snuke' n = x : (snuke' (x+1))
      where
        x = minimumBy (\a b -> compare (f a) (f b)) $ map (\d -> 10^(d+1) * floor((fromIntegral n) % (10^(d+1)) + 1) - 1) [0..(ceiling (logBase 10 (fromIntegral n)) + 1)]
        
    s n
      | n <= 9 = n
      | otherwise = (mod n 10) + s (div n 10)
    f n = (fromIntegral n) / (fromIntegral $ s n)