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)


from functools import lru_cache

@lru_cache(maxsize=10000)
def calc(n, k):
    # print(n, k)

    if n < 10:
        if k > 1:
            # print('1:return 0')
            return 0
        elif k == 1:
            # print('2:return ' + str(n))
            return n
        else:
            return 1

    else:
        if k == 0:
            # print('5:return ')
            return 1#calc(n // 10, k)
        else:
            # print('6:return ')
            return calc(n // 10, k - 1) * (n % 10) + calc(n // 10 - 1, k - 1) * (9 - n % 10) + calc(n // 10, k)

n = int(input())
k = int(input())

print(calc(n, k))