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: Wrong Answer)

import math
def comb(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

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

def calc(i, k):
    return comb(len(n) - i - 1, k) * 9 ** k

def cnt(n):
    ret = 0
    for c in n:
        if c != '0':
            ret += 1
    return ret

ans = 0
# if len(n) == k and cnt(n) == k:
#     ans +=1

for i in range(min(len(n), k)):
    if int(n[i]) == 0:
        continue
    if len(n)-i > k:
        print(calc(i, k))
        ans += calc(i, k)
    k -= 1
    if len(n)-i > k:
        ans += (int(n[i]) - 1) * calc(i, k)
    if k == 0:
        ans += 1
print(ans)