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 Python (3.4.3) (judge verdict: Accepted)

import math
def check1(N):
    if N == 0:
        return 0
    n = int(math.log10(N))
    return 9*n+(N//(10**n))
def check2(N):
    if N == 0:
        return 0
    n = int(math.log10(N))
    return n*(n-1)/2*81+(N//(10**n)-1)*n*9+check1(N%(10**n))
def check3(N):
    if N == 0:
        return 0
    n = int(math.log10(N))
    summ = 0
    if n >= 3:
        for i in range(n):
            summ += i*(i-1)/2
    return summ*729+(N//(10**n)-1)*n*(n-1)/2*81+check2(N%(10**n))
def main():
    N = int(input())
    K = int(input())
    if K == 1:
        print(int(check1(N)))
    elif K == 2:
        print(int(check2(N)))
    elif K == 3:
        print(int(check3(N)))
        
main()