Hieroglyphs

문제

A team of researchers is studying the similarities between sequences of hieroglyphs. They represent each hieroglyph with a non-negative integer. To perform their study, they use the following concepts about sequences.

For a fixed sequence $AA$, a sequence $SS$ is called a subsequence of $AA$ if and only if $SS$ can be obtained by removing some elements (possibly none) from $AA$.

The table below shows some examples of subsequences of a sequence $A=[3,2,1,2]A\; =\; [3,\; 2,\; 1,\; 2]$.

Subsequence	How it can be obtained from $AA$
$[3,2,1,2][3,\; 2,\; 1,\; 2]$	No elements are removed.
$[2,1,2][2,\; 1,\; 2]$	$[\text{enclose}horizontalstrike3,2,1,2][\backslash enclose\{horizontalstrike\}\{3\},\; 2,\; 1,\; 2]$
$[3,2,2][3,\; 2,\; 2]$	$[3,2,\text{enclose}horizontalstrike1,2][3,\; 2,\; \backslash enclose\{horizontalstrike\}\{1\},\; 2]$
$[3,2][3,\; 2]$	$[3,\text{enclose}horizontalstrike2,\text{enclose}horizontalstrike1,2][3,\; \backslash enclose\{horizontalstrike\}\{2\},\; \backslash enclose\{horizontalstrike\}\{1\},\; 2]$ or $[3,2,\text{enclose}horizontalstrike1,\text{enclose}horizontalstrike2][3,\; 2,\; \backslash enclose\{horizontalstrike\}\{1\},\; \backslash enclose\{horizontalstrike\}\{2\}]$
$[3][3]$	$[3,\text{enclose}horizontalstrike2,\text{enclose}horizontalstrike1,\text{enclose}horizontalstrike2][3,\; \backslash enclose\{horizontalstrike\}\{2\},\; \backslash enclose\{horizontalstrike\}\{1\},\; \backslash enclose\{horizontalstrike\}\{2\}]$
$[][\; ]$	$[\text{enclose}horizontalstrike3,\text{enclose}horizontalstrike2,\text{enclose}horizontalstrike1,\text{enclose}horizontalstrike2][\backslash enclose\{horizontalstrike\}\{3\},\; \backslash enclose\{horizontalstrike\}\{2\},\; \backslash enclose\{horizontalstrike\}\{1\},\; \backslash enclose\{horizontalstrike\}\{2\}]$

On the other hand, $[3,3][3,\; 3]$ or $[1,3][1,\; 3]$ are not subsequences of $AA$.

Consider two sequences of hieroglyphs, $AA$ and $BB$. A sequence $SS$ is called a common subsequence of $AA$ and $BB$ if and only if $SS$ is a subsequence of both $AA$ and $BB$. Moreover, we say that a sequence $UU$ is a universal common subsequence of $AA$ and $BB$ if and only if the following two conditions are met:

• $UU$ is a common subsequence of $AA$ and $BB$.
• Every common subsequence of $AA$ and $BB$ is also a subsequence of $UU$.

It can be shown that any two sequences $AA$ and $BB$ have at most one universal common subsequence.

The researchers have found two sequences of hieroglyphs $AA$ and $BB$. Sequence $AA$ consists of $NN$ hieroglyphs and sequence $BB$ consists of $MM$ hieroglyphs. Help the researchers compute a universal common subsequence of sequences $AA$ and $BB$, or determine that such a sequence does not exist.