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: Wrong Answer)


def solve(p,n,k):
    if k==1:
        return 10 + 9*(n-1)+(p-1)
    elif k==2:
        return 81 * n*(n-1)//2 + (p-1)*9*n
    else:
        return 729 * n*(n-1)*(n-2)//6 + (p-1)*81*n*(n-1)//2

N=input()
K=int(input())
dig = len(N) - 1

try:
    if K == 2:
        print(solve(int(N[0]),dig,2) + solve(int(N[1]),dig-1,1))
    elif K == 3:
        print(solve(int(N[0]),dig,3) + solve(int(N[1]),dig-1,2) + solve(int(N[2]),dig-2,1))
    elif K == 1:
        print(solve(int(N[0]),dig,1))
except:
    print(0)