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: Wrong Answer)

from bisect import *
from collections import *
from fractions import gcd
from math import factorial
def permutations_count(n, r):
    if not n>=r>=0:
        return(0)
    else:
        return factorial(n) // factorial(n - r)
def combinations_count(n, r):
    if not n>=r>=0:
        return(0)
    else:
        return factorial(n) // (factorial(n - r) * factorial(r))
N=input()
K=int(input())

length=len(str(N))
count=0
count3=0
for i in range(length):
    if N[i]!=0:
        count+=combinations_count(length-1-count3,K-count3)*(9**(K-count3))
        count+=combinations_count(length-1-count3,K-count3-1)*(9**(K-1-count3))*(int(N[i])-1)
        count3+=1
        if K-count3==0:
            count+=1
            break

if count<0:
    count=0
print(count)