wavynumbers

Wavy Numbers

A wavy number is a positive integer that for any digit of its decimal representation, the following condition holds: The digit is either strictly larger than all adjacent digits or strictly smaller than all adjacent digits. For example, numbers $35270$, $102$, $747$, $20$ and $3$ are wavy but numbers $123$, $1000$, $2212$, and $55$ are not.

The task is to find the $k^{th}$ smallest wavy number $r$ that is divisible by $n$, for the given integer values $n$ and $k$.

You are to write a program that will find the value of $r$ if it doesn't exceed ${10}^{14}$.

Input format

The only line of input contains two integers $n$ and $k$, separated by a single space.

Output format

Output a single integer $r$ — the answer to the given problem. If such a number does not exist or it is larger than ${10}^{14}$, then print "-1" (negative one without the quotes) instead.

Limits

Samples

The values of the first four wavy numbers that are divisible by $123$ are: $492$, $615$, $738$ and $1845$.