Problem:
Score : 500 points

Problem Statement

Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.

Constraints

1 \leq N < 10^{100}

1 \leq K \leq 3

Input

Input is given from Standard Input in the following format:

N
K

Output

Print the count.

Sample Input 1

100
1

Sample Output 1

19

The following 19 integers satisfy the condition:

1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100

Sample Input 2

25
2

Sample Output 2

14

The following 14 integers satisfy the condition:

11,12,13,14,15,16,17,18,19,21,22,23,24,25

Sample Input 3

314159
2

Sample Output 3

937

Sample Input 4

9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
3

Sample Output 4

117879300

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

import Data.List
main :: IO ()
main = do
  [maxVal] <- getInts
  [numOfNonZero] <- getInts
  print $ length $ search numOfNonZero [1..maxVal]

search :: Int -> [Int] -> [Int]
search numOfNonZero = filter $ hasNonZeroIs numOfNonZero

hasNonZeroIs :: Int -> Int -> Bool
hasNonZeroIs nonZeroNum num = (numOfNonZero == nonZeroNum)
  where
    numOfNonZero = foldl (\s n -> if n /= '0' then s + 1 else s) 0 $ show num 

getInts = do
  x <- getLine
  let y = (map $ read) $ words x :: [Int]
  return y