E - Digit Products

Score : $500$ points

Problem Statement

For how many positive integers at most $N$ is the product of the digits at most $K$?

Constraints

• $1 \leq N \leq 10^{18}$
• $1 \leq K \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$

Output

Print the number of integers satisfying the condition.

13 2

5

Out of the positive integers at most $13$, there are five such that the product of the digits is at most $2$: $1$, $2$, $10$, $11$, and $12$.

100 80

99

Out of the positive integers at most $100$, all but $99$ satisfy the condition.

1000000000000000000 1000000000

841103275147365677

Note that the answer may not fit into a $32$-bit integer.