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 8.8.3) (judge verdict: Accepted)

import Data.Char
main=print.solve.(\[n,k]->(n,read k)).lines=<<getContents
solve(n,k)=(!!k).fst.foldr f((\a->(a,a))$1:replicate k 0)$map digitToInt n
f i(rs,as)=case i of
  0->(rs,bs)
  i->(mul(i-1)as`add`(0:rs)`add`as,bs)
  where bs=as`add`mul 9 as
add=zipWith(+)
mul k as=0:map(*k)as