Denis, Vanya and Fedya gathered at their first team training. Fedya
told them that he knew the algorithm for constructing a
Gray code.

Create a 2bit list: {0, 1}.

Reflect this list and concatenate it with the original list: {0, 1, 1, 0}.

Prefix old entries with 0, and prefix new entries with 1: {00, 01, 11, 10}.

Repeat steps 2 and 3 until the length of all elements is equal to n.
The number
n is a
length of a Gray code. For example, the code
of length 3 is: {000, 001, 011, 010, 110, 111, 101, 100}.
Denis ran the Fedya's algorithm and obtained a binary number x
at position k (positions are numbered starting from zero).
Vanya wrote down the numbers k and x in binary system.
This story happened many years ago and now you hold the paper sheet
with these numbers in your hands. Unfortunately, some digits are unreadable
now. Could you determine the values of these digits using the readable digits?
Input
The first line contains a number k written in the binary system.
Unreadable digits are denoted with symbol “?”. The second line contains
a number x in the same format. The lengths of these numbers are
equal and don't exceed 10^{5}. The numbers may contain leading zeroes.
Output
If there is a unique way to restore the numbers k and
x, output them, replacing the symbols “?” with “0” or “1”.
If there are multiple ways to restore them, output “Ambiguity”.
If Denis or Vanya certainly made a mistake in these numbers, output
“Impossible”.
Samples
input  output 

0?1
0?0
 011
010

?00
??0
 Ambiguity

100
100
 Impossible 
Problem Author: Dmitry Poletaev
Problem Source: XV Open USU Championship