You are given a positive integer n. The beauty factor of a number is the sum of digits obtained till the obtained sum is a single digit.

Example

• Beauty factor of 1987 = 1+9+8+7 = 25 = 2+5 = 7
• Beauty factor of 10 = 1+0 = 1

You are given a beauty factor, \(b\). Your task is to find a minimum number (\(n\)) of length \(k\) whose beauty factor is \(b\).

Here, the length of a number is defined as the number of digits a number has. 

Note: The digits of the number in the output must be distinct and must be a positive integer

Input format

The first line contains the beauty factor \(b\) \((0 < b < 10)\) and the length of a number \(k\) \((0 < k < 10)\).

Output format

Print the minimum number of length \(k\) whose beauty factor is \(b\). If no such number is possible to make the beauty factor \(b\) with length \(k\), then print \(-1\).