A13205. M-numbers

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.