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)

from math import factorial

def combinations_count(n, r):
    return factorial(n) // (factorial(n - r) * factorial(r))

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


ans = 0

if len(str(n)) < k:
    print(0)
    exit()

def ans1(n,k):
    global ans
    m = len(str(n))
    if m-1 >= k:
        ans += combinations_count(m-1, k) * 9 ** k

    if m >= k:
        ans += (int(str(n)[0])-1) * combinations_count(m-1, k-1) * 9 ** (k-1)
        if k >= 2 and m > 1:
            ans1(int(str(n)[1:]), k-1)
        elif k == 1:
            ans += 1

ans1(n,k)

print(ans)