E - Almost Everywhere Zero

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.

100
1

19

The following $19$ integers satisfy the condition:

• $1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100$

25
2

14

The following $14$ integers satisfy the condition:

• $11,12,13,14,15,16,17,18,19,21,22,23,24,25$

314159
2

937

9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
3

117879300