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)

n = input()
k = int(input())
l = len(n)

def k2(l, n):
    ans = 81 * (l - 1) * (l - 2) // 2
    ans += (int(n[0]) - 1) * 9 * (l - 1)
    for i, s in enumerate(n[1:]):
        if s == "0":
            continue
        ans += int(s)
        ans += max((l - i - 2), 0) * 9
        break
    return ans

if k == 1:
    ans = (l - 1) * 9 + int(n[0])
elif k == 2:
    if l == 1:
        print(0)
        exit()
    ans = k2(l, n)
else:
    if l < 3:
        print(0)
        exit()
    ans = 9 ** 3 * (l - 1) * (l - 2) * (l - 3) // 6
    ans += (int(n[0]) - 1) * 81 * (l - 1) * (l - 2) // 2
    n = n[1:]
    n = str(int(n))
    ans += k2(len(n), n)
print(ans)