A9943 | Equidistant String

Little Susie loves strings. Today she calculates distances between them. As Susie is a small girl after all, her strings contain only digits zero and one. She uses the definition of Hamming distance:

We will define the distance between two strings $s$ and $t$ of the same length consisting of digits zero and one as the number of positions $i$ , such that $s_{i}$ isn't equal to $t_{i}$ .

As besides everything else Susie loves symmetry, she wants to find for two strings $s$ and $t$ of length $n$ such string $p$ of length $n$ , that the distance from $p$ to $s$ was equal to the distance from $p$ to $t$ .

It's time for Susie to go to bed, help her find such string $p$ or state that it is impossible.

The first line contains string $s$ of length $n$ .

The second line contains string $t$ of length $n$ .

The length of string $n$ is within range from $1$ to $10^{5}$ . It is guaranteed that both strings contain only digits zero and one.

Print a string of length $n$ , consisting of digits zero and one, that meets the problem statement. If no such string exist, print on a single line "impossible" (without the quotes).

If there are multiple possible answers, print any of them.