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 (3.4.3) (judge verdict: Accepted)

n=int(input())
k=int(input())
d=len(str(n))
from math import factorial as f
def c(n):
  if n<2:
    return 0
  else:
    return f(n)//(f(n-2)*f(2))
def kk(n):
  dd=len(str(n))
  s=9*(dd-1)
  s+=int(str(n)[0])
  return s
def kkk(n):
  d=len(str(n))
  s=81*(d-1)*(d-2)//2
  s+=9*(d-1)*(int(str(n)[0])-1)
  s+=kk(int(str(n)[1:]))
  return s

if d==1 and k!=1:
  print(0)
else:
  if k==1:
    ans=kk(n)
  elif k==2:
    ans=kkk(n)
  else:
    t=0
    for i in range(2,d-1):
      t+=c(i)
    ans=729*t
    ans+=81*c(d-1)*(int(str(n)[0])-1)
    ans+=kkk(int(str(n)[1:]))
  print(ans)