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 (2.4.0) (judge verdict: Time Limit Exceeded)

import math
import itertools
n=int(input())
k=int(input())
def comb(n,k):
    return len(list(itertools.combinations(range(n), k)))
x=str(n)
m=len(x)
ans=0
for i in range(1,m):
    ans+=(comb(i-1,k-1)*(9**k))
if k==1:
    for i in range(1,10):
        if i*(10**(m-1))<=n:
            ans+=1
elif k==2:
    for i in range(1,10):
        if i*(10**(m-1))<=n:
            for j in range(m-1):
                for a in range(1,10):
                    if i*(10**(m-1))+a*(10**(j))<=n:
                        ans+=1
                    else:
                        break
        else:
            break
else:
    for i in range(1,10):
        if i*(10**(m-1))<=n:
            for j in range(m-1):
                for a in range(1,10):
                    if i*(10**(m-1))+a*(10**(j))<=n:
                        for b in range(j):
                            for c in range(1,10):
                                if i*(10**(m-1))+a*(10**(j))+c*(10**(b))<=n:
                                    ans+=1
                                else:
                                    break
                    else:
                        break
        else:
            break
print(ans)