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)

n=input()
ln=len(n)
nn=[-1,-1,-1]
nnn=[0,0,0]
j=0
for i in range(ln):
  if n[i]!="0":
    nn[j]=i
    nnn[j]=int(n[i])
    j+=1
    if j==3:
      break

s=[9*(ln-1),81*(ln-1)*(ln-2)//2,729*(ln-1)*(ln-2)*(ln-3)//6]
s[0]+=nnn[0]
s[1]+=(nnn[0]-1)*9*(ln-1)+(0 if nn[1]==-1 else nnn[1]+9*(ln-nn[1]-1))
s[2]+=(nnn[0]-1)*81*(ln-1)*(ln-2)//2
s[2]+=(0 if nn[1]==-1 else (nnn[1]-1)*9*(ln-nn[1]-1)+81*(ln-nn[1]-1)*(ln-nn[1]-2)//2)+(0 if nn[2]==-1 else nnn[2]+9*(ln-nn[2]-1))

k=int(input())
print(s[k-1])