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 (3.8.2) (judge verdict: Accepted)

import sys

read = sys.stdin.read


def main():
    N, K = map(int, read().split())

    dp1 = [0] * (K + 1)
    dp2 = [0] * (K + 1)
    dp1[0] = 1

    for x in map(int, str(N)):
        for j in range(K, -1, -1):
            if j > 0:
                dp2[j] += dp2[j - 1] * 9
                if x != 0:
                    dp2[j] += dp1[j - 1] * (x - 1) + dp1[j]
                    dp1[j] = dp1[j - 1]
            else:
                dp1[j] = 0
                dp2[j] = 1

    print(dp1[K] + dp2[K])
    return


if __name__ == '__main__':
    main()