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=int(input())
k=int(input())
l=[int(i) for i in "0"+str(n)]
# [0]=n [1]<n
dp=[[[0]*5,[0]*5] for i in "ww"]
dp[0][0][0]=1
for i,j in enumerate(str(n)):
    i+=1
    for p in range(k+1):
        if dp[i%2-1][0][p]:
            dp[i%2][0][p+[0,1][l[i]>0]]=1
            for q in range(l[i]):
                dp[i%2][1][p+[0,1][q>0]]+=1
        if dp[i%2-1][1][p]:
            dp[i%2][1][p]+=dp[i%2-1][1][p]
            dp[i%2][1][p+1]+=dp[i%2-1][1][p]*9
    for p in range(10): dp[i%2-1][p//5][p%5]=0
print(dp[0][0][k]+dp[1][0][k]+dp[0][1][k]+dp[1][1][k])