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: Wrong Answer)

N=int(input())
K=int(input())
if N<=10**6:
  ans=0
  for i in range(1,N+1):
    a=str(i)
    if len(a)-list(a).count("0")==K:
      ans+=1
  print(ans)
  #exit()
if K==1:#おけ
  ans=0
  print((len(str(N))-1)*9+int(str(N)[0]))
elif K==2:#おけ
  ans=0
  L=list(map(int,list(str(N))))
  for i in range(len(L)-1):
    ans+=(9*(int(str(N)[0])-1))
    for j in range(i+1,len(L)):
      if i==0:
        if j==1:
          ans+=int(str(N)[1])
        else:
          ans+=9
      else:
        ans+=81
  print(ans)
else:
  ans=0
  L=list(map(int,list(str(N))))
  le=len(L)
  for i in range(le-2):
    for j in range(i+1,le-1):
      for k in range(j+1,le):
        if i==0:
          ans+=81*(int(str(N)[0])-1)
          if j==1:
            ans+=9*(int(str(N)[1])-1)
            if k==2:
              ans+=int(str(N)[2])
            else:
              ans+=9
          else:
            ans+=81
        else:
          ans+=729
  print(ans)