Unusual Number

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.

Medium6MathNumber theoryImplementationBrute forceNo attempts yetTime limit2sMemory limit512 MB

Description

Examples3

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.