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 itertools import combinations
N = list(map(int, input()))
K = int(input())

nlen = len(N)
ans = 0
if K <= nlen:
    cmb = [9] * nlen
    for n in N:
        if n != 0:
            cmb[0] = n - 1
            for x in combinations(cmb, K):
                y = x[0]
                for z in x[1:]:
                    y *= z
                ans += y
            if K == 1:
                ans += 1
                break
            K -= 1
        cmb.pop()
print(ans)