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.

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.

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