G. M-numbers
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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.

Examples
Input
24 9

Output
226

Input
24 1

Output
38

Input
5040 1000000000

Output
111121111315213227111

Input
2020 2020

Output
-1