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.Char
main :: IO ()
main = do
    k <- readLn
    mapM_ print $ solve k

sn :: Int -> Int
sn = sum . map digitToInt . show

nDivSn :: Int -> Float
nDivSn n = (fromIntegral n) / (fromIntegral (sn n))

solve :: Int -> [Int]
solve k = take k $ sunuke 0 1

sunuke n diff
    | xf < yf   = x : (sunuke x diff)
    | otherwise = y : (sunuke y (diff*10))
        where x = n + diff
              y = n + diff*10
              xf = nDivSn x
              yf = nDivSn y