In your factory, you are making two kinds of colored paper, one colored red, and the other colored blue.

Each red-colored paper has a string $$$S$$$ written on it: it is made of $$$|S|$$$ unit squares in a row, and $$$S_i$$$ is written on the $$$i$$$-th square from the left.

Each blue-colored paper has a string $$$T$$$ written on it: it is made of $$$|T|$$$ unit squares in a row, and $$$T_i$$$ is written on the $$$i$$$-th square from the left.

You plan to make a new kind of paper called double-colored paper out of red and blue paper. To do so, you will cut a piece of red paper to leave a continuous part with positive integer length, then do the same with a piece of blue paper. After that, you will glue the end of the red piece to the start of the blue piece.

For example, suppose $$$S$$$ is abcde and $$$T$$$ is fghij. You can make a double-colored paper with string $$${\color{red}{\underline{\texttt{bcd}}}}{\color{blue}{\texttt{fg}}}$$$ or $$${\color{red}{\underline{\texttt{abc}}}}{\color{blue}{\texttt{ij}}}$$$ written on it. However, you cannot make a double-colored paper with string $$${\color{red}{\underline{\texttt{acd}}}}{\color{blue}{\texttt{ghij}}}$$$ or $$${\color{blue}{\texttt{fghij}}}$$$ written on it. (Here the underlined string denotes a red piece, and the rest denotes a blue piece.) Two pieces of double-colored paper are considered the same if they have the same red string and the same blue string written on them.

Among all different pieces of double-colored paper that can be made, you want to know the one with the lexicographically $$$K$$$-th smallest string written on it. Note that there may be papers with the same strings written on them, but with different lengths of red paper: in this case, you may order them arbitrarily.