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)

def nCk(n, k):
    if n < k:
        return 0
    elif k == 0:
        return 1
    elif k == 1:
        return n
    elif k == 2:
        return n * (n - 1) // 2
    else:
        return n * (n - 1) * (n - 2) // 6


def solve(N, K):
    if K == 0:
        return 1

    M = len(N)
    if M < K:
        return 0

    x = int(N[0])

    res = 0
    if x != 0:
        res += solve(N[1:], K - 1)
        res += (x - 1) * nCk(M - 1, K - 1) * (9 ** (K - 1))
    res += nCk(M - 1, K) * (9 ** K)

    return res


N = input()
K = int(input())

print(solve(N, K))