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: Runtime Error)

n = input()
k = int(input())

import math

def func(n,k):
  if k==0:
    return 0
  digit = len(n)
  res = 0
  if digit == 1:
    if k ==1:
      res = int(n)
    return res
  if digit == 2:
    if k ==2:
      res = (int(n) - 9 - int(n) //10)
    elif k == 3:
      res = (0)
    else:
      res = (9+int(n)//10)
    return res

  base = 9**k * (math.factorial(digit-1)/ (math.factorial(k) * math.factorial(digit-1-k)) )

  for i in range(9):
    i+= 1
    if i < int(n[0]):
      base += func(n[1:],k-1)
  return base

print(int(func(n,k)))