M-numbers
Description
For a given positive integer $m$, a positive number is called a $m$-number if the product of its digits is $m$. For example, the beginning of a series of $24$-numbers are as follows: $38$, $46$, $64$, $83$, $138$, $146$, $164$, $183$, $226$ ...
You are given a positive integer $m$ and $k$. Print $k$-th among $m$-numbers if all $m$-numbers are sorted in ascending order.
A single line of input contains two integers $m$ and $k$ ($2 \le m \le 10^9$, $1 \le k \le 10^9$).
Print the desired number — $k$-th among all $m$-numbers if $m$-numbers are sorted in ascending order. If the answer does not exist, print -1.
Input
A single line of input contains two integers $m$ and $k$ ($2 \le m \le 10^9$, $1 \le k \le 10^9$).
Output
Print the desired number — $k$-th among all $m$-numbers if $m$-numbers are sorted in ascending order. If the answer does not exist, print -1.
Samples
24 9
226
24 1
38
5040 1000000000
111121111315213227111
2020 2020
-1