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 PyPy3 (2.4.0) (judge verdict: Accepted)

n = input().strip()
k = int(input().strip())
le = len(n)
dp = [[[0] * 2 for _ in range(5)] for _ in range(101)]
dp[0][0][0] = 1

for i in range(le):
    for cnt in range(4):
        for smaller in range(2):
            fig = int(n[i])
            for d in range(10):
                tmp1 = i + 1
                tmp2 = cnt
                tmp3 = smaller
                if d != 0:
                    tmp2 += 1
                if k < cnt:
                    continue
                if smaller == 0:
                    if fig < d:
                        continue
                    elif d < fig:
                        tmp3 = 1
                dp[tmp1][tmp2][tmp3] += dp[i][cnt][smaller]
print(dp[le][k][0] + dp[le][k][1])