CF545B.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.

小苏西喜欢字符串。今天她计算字符串之间的距离。由于苏西毕竟还是个小女孩，她的字符串只包含数字 0 和 1。她使用汉明距离（Hamming distance）的定义：

我们将两个等长字符串 $s$ 和 $t$（均由数字 0 和 1 组成）之间的距离定义为满足 $s_i \ne t_i$ 的位置 $i$ 的个数。

此外，由于苏西还特别喜爱对称性，她希望对两个长度为 $n$ 的字符串 $s$ 和 $t$，找到一个长度同样为 $n$ 的字符串 $p$，使得 $p$ 到 $s$ 的距离等于 $p$ 到 $t$ 的距离。

现在到了苏西该睡觉的时间了，请你帮她找出这样的字符串 $p$，或者说明其不存在。

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 105. It is guaranteed that both strings contain only digits zero and one.

第一行包含一个长度为 $n$ 的字符串 $s$。
第二行包含一个长度为 $n$ 的字符串 $t$。
字符串长度 $n$ 的取值范围为 $1$ 到 $10^5$。保证两个字符串仅由数字 0 和 1 组成。

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.

输出一个长度为 $n$ 的字符串，该字符串仅由数字 0 和 1 组成，且满足题目要求。如果不存在这样的字符串，则在单独一行中输出 "impossible"（不带引号）。

如果存在多个可能的答案，输出其中任意一个即可。

In the first sample different answers are possible, namely — 0010, 0011, 0110, 0111, 1000, 1001, 1100, 1101.

在第一个样例中，存在多种可能的答案，即：0010、0011、0110、0111、1000、1001、1100、1101。