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()
K = int(input())

length = len(S)
dp = [[[0] * (K + 1) for _ in range(2)] for _ in range(length + 1)]
dp[0][0][0] = 1

for i in range(1, length + 1):
    for j in range(2):
        for k in range(K + 1):
            os = int(S[i - 1])
            for x in range(10):
                ni = i
                nj = j
                nk = k
                if x != 0:
                    nk += 1
                if nk > K:
                    continue
                if j == 0:
                    if x > os:
                        continue
                    elif x < os:
                        nj = 1
                dp[ni][nj][nk] += dp[i - 1][j][k]

ans = dp[length][0][K] + dp[length][1][K]
print(ans)