Problem:
Score : 400 points

Problem Statement

A positive integer X is said to be a lunlun number if and only if the following condition is satisfied:

In the base ten representation of X (without leading zeros), for every pair of two adjacent digits, the absolute difference of those digits is at most 1.

For example, 1234, 1, and 334 are lunlun numbers, while none of 31415, 119, or 13579 is.

You are given a positive integer K. Find the K-th smallest lunlun number.

Constraints

1 \leq K \leq 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

K

Output

Print the answer.

Sample Input 1

15

Sample Output 1

23

We will list the 15 smallest lunlun numbers in ascending order:

1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
21,
22,
23.

Thus, the answer is 23.

Sample Input 2

1

Sample Output 2

1

Sample Input 3

13

Sample Output 3

21

Sample Input 4

100000

Sample Output 4

3234566667

Note that the answer may not fit into the 32-bit signed integer type.

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import           Control.Monad
import           Control.Monad.ST
import qualified Data.Array                  as A
import qualified Data.Array.ST               as ST
import qualified Data.Array.Unboxed          as AU
import           Data.Bits
import qualified Data.ByteString.Char8       as BS
import           Data.Char
import           Data.Int
import qualified Data.IntMap                 as IM
import           Data.List
import qualified Data.Map                    as M
import           Data.Maybe
import           Data.Ord
import qualified Data.Set                    as S
import           Data.Time
import qualified Data.Vector                 as V
import qualified Data.Vector.Mutable         as VM
import qualified Data.Vector.Unboxed         as VU
import qualified Data.Vector.Unboxed.Mutable as VUM

readInt :: IO [Int]
readInt = map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine

readInts :: Int -> IO [[Int]]
readInts n = replicateM n readInt

readInteger :: IO [Integer]
readInteger = map (fst . fromJust . BS.readInteger) . BS.words <$> BS.getLine

readIntegers :: Int -> IO [[Integer]]
readIntegers n = replicateM n readInteger

readString :: IO [String]
readString = map BS.unpack . BS.words <$> BS.getLine

readStrings :: Int -> IO [[String]]
readStrings n = replicateM n <$> readString

toPair :: [a] -> (a, a)
toPair [x, y] = (x, y)

count :: Eq a => a -> [a] -> Int
count a as = length $ filter (== a) as

main = do
  [k] <- readInt
  print $ lunlun !! (k - 1)

lunlun = [1 .. 9] ++ concatMap f lunlun

f n
  | m == 0 = [10 * n + m, 10 * n + m + 1]
  | m == 9 = [10 * n + m - 1, 10 * n + m]
  | otherwise = [10 * n + m - 1, 10 * n + m, 10 * n + m + 1]
  where
    m = n `mod` 10