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)

#!/usr/bin/env python3

from copy import deepcopy

def main():
    n = input()
    l = len(n)
    k = int(input())
    dp0 = [0 for j in range(4)]
    dp1 = [0 for j in range(4)]
    dp1[0] = 1
    for i in range(l):
        dppre0 = deepcopy(dp0)
        dppre1 = deepcopy(dp1)
        d = int(n[i])
        if d == 0:
            for j in [1, 2, 3]:
                dp0[j] += dppre0[j - 1] * 9
        else:
            for j in [1, 2, 3]:
                dp0[j] += dppre0[j - 1] * 9
                dp0[j] += dppre1[j - 1] * max(0, d - 1)
            for j in [0, 1, 2, 3]:
                dp0[j] += dppre1[j]
            dp1 = [0 for j in range(4)]
            for j in [1, 2, 3]:
                dp1[j] = dppre1[j - 1]
    print(dp0[k] + dp1[k])

if __name__ == "__main__":
    main()