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)

import sys
from functools import lru_cache

read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 9)
INF = 1 << 60
MOD = 1000000007


def com(n, r):
    if n < r or n < 0 or r < 0:
        return 0
    r = min(r, n - r)
    numer = denom = 1
    for i in range(n - r + 1, n + 1):
        numer = numer * i
    for i in range(1, r + 1):
        denom = denom * i
    return numer // denom


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

    S = str(N)
    L = len(S)

    @lru_cache(maxsize=None)
    def rec(i, k, smaller):
        if i == L:
            if k == 0:
                return 1
            else:
                return 0
        if k == 0:
            return 1
        if smaller:
            return com(L - i, k) * pow(9, k)
        if S[i] == '0':
            return rec(i + 1, k, False)

        ans = 0
        ans += rec(i + 1, k, True)
        ans += rec(i + 1, k - 1, True) * (int(S[i]) - 1)
        ans += rec(i + 1, k - 1, False)
        return ans

    ans = rec(0, K, False)

    print(ans)
    return


if __name__ == '__main__':
    main()