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 PyPy3 (7.3.0) (judge verdict: Accepted)

from functools import lru_cache
import sys
sys.setrecursionlimit(10 ** 5 + 10)


def input(): return sys.stdin.readline().strip()


def resolve():

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

    @lru_cache(None)
    def F(n, k):

        if n < 10:
            if 1 < k:
                return 0
            elif k == 1:
                return n
            elif k == 0:
                return 1

        m, r = divmod(n, 10)
        ret = 0
        # rに応じて場合分け
        if k >= 1:
            ret += F(m, k-1)*r  # r<=k
            ret += F(m-1, k-1)*(9-r)  # r>k
        ret += F(m, k)*1  # r==0
        return ret
    print(F(n, k))


resolve()