Unusual Number

Time limit2sMemory limit512 MB

Summary

Given digit count a and multiplier b, find the smallest a-digit number whose last digit moved to the front equals b times the number, or report Impossible.

Level: Medium6 of 10
Topics: Math, Number theory, Implementation, Brute force
Solved: No attempts yet

Problem

A positive integer $N$ is an unusual number when it satisfies both of the conditions below.

$N$ has $a$ digits and its leading digit is not 0.
Let $N'$ be the number formed by moving the last digit of $N$ to the front. Then $N' = b \times N$ .

Given $a$ and $b$ , find the smallest unusual number.

Input

The first line contains $a$ and $b$ , separated by a single space. ( $1 \le a \le 10^6$ , $1 \le b \le 9$ )

Output

Print the smallest unusual number on the first line. If no number satisfies the conditions, print Impossible.

Examples3

Example 1
Input
```
3 1
```
Expected output
```
111
```
Example 2
Input
```
1 3
```
Expected output
```
Impossible
```
Example 3
Input
```
12 4
```
Expected output
```
102564102564
```