Given two strings of lowercase letters, $a$ and $b$, print the shortest string $x$ of lowercase letters such that exactly one (but not both) of $ax$ or $bx$ is a palindrome; that is, equal to itself when reversed.
Standard input contains several pairs of $a$ and $b$ (at most $500$). Each string is on a separate line and consists of between $0$ and $1\, 000$ lowercase letters.
For each pair, output a line containing $x$. If several $x$ satisfy the criteria above, choose the first one in alphabetical order. If no such string $x$ exists, print “No solution.” as answer.
|Sample Input 1||Sample Output 1|
abab ababab abc def