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: Wrong Answer)

N = input()
K = int(input())

def c(i, j):
    i, j = i-1, j-1
    if j == 0:
        return 1
    r = 1
    for k in range(j):
        r *= (i-k) / (j-k)
    return int(r)


def d(n, k):
    if K == 1:
        return int(N[0])
    if K == 3:
        return int(N[0]) * int(N[1]) * int(N[2])
    if K == 2:
        return (int(N[0])-1) * 9 + int(N[1])


ans = 0
l = len(N)
for i in range(K, l+1):
    if i == l:
        ans += max(0,(c(i, K)-1))*9**(K-1)*int(N[0]) + d(N,K)
    else:
        ans += c(i, K) * 9**K
    
print(ans)