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)

s = input()
n = len(s)
k = int(input())

dp = [[[0 for _ in range(2)] for _ in range(k + 1)] for _ in range(n + 1)]
dp[0][0][0] = 1

for l in range(n):
    for m in range(k + 1):
        for o in range(2):
            nd = int(s[l])
            for d in range(10):
                nl, nm, no = l + 1, m, o
                if d != 0:
                    nm += 1
                if nm > k:
                    continue
                if 0 == o:
                    if d > nd:
                        continue
                    if d < nd:
                        no = 1
                dp[nl][nm][no] += dp[l][m][o]
print(sum(dp[-1][-1]))