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())
from functools import lru_cache

@lru_cache(maxsize=1000)
def dp(n, k): #0以上n以下の数で０でない数字がちょうどk個あるもの。
  if k == 0:
    return 1
  elif n == 0:
    return 0
  else:
    n = int(n)
    s = str(n)
    digit = len(s)
    m, fdigit = divmod(n,10)
    if m >= 1:
        return int(dp(m, k-1) * fdigit + dp(m-1, k-1)* (9-fdigit) + dp(m, k))
    elif k == 1:
        return n
    elif k == 2 or k == 3:
        return 0
    else:
        return 1
if K == 0:
    answer = dp(N, K)-1
else:
    answer = dp(N, K)
print(int(answer))