Finding a Friend's Name

Chulsoo wants to determine the name of student number $n$ in Class 6 of the second grade. He obtained the roster of all $m$ students in the class, except that the name of student number $n$ is missing.

Student numbers in the class are assigned after sorting all names in Korean lexicographic order. No two students have the same name.

Every name consists only of precomposed Hangul syllables. Names are compared syllable by syllable from left to right. At the first differing syllable, the name containing the earlier syllable comes first. If one name is a prefix of the other, the shorter name comes first. The syllable order is the Unicode order 가, 각, $\cdots$, 힣.

Chulsoo has the names of the other students in Class 6 and the roster of every second-grade student.

Find every second-grade student's name that could be the name of student number $n$ in Class 6.

The input is given in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$

Each case is given in the following format:

$n\ m\ k$ $a_1$ $a_2$ $\vdots$ $a_{m-1}$ $b_1$ $b_2$ $\vdots$ $b_k$

$a_1,a_2,\cdots,a_{m-1}$ are the names of the students in Class 6 other than the student whose name is missing, given in Korean lexicographic order. If $m=1$, this part contains no names.

$b_1,b_2,\cdots,b_k$ are the names of all second-grade students, given in Korean lexicographic order.

For each test case, first print the number $c$ of possible names.

Then print the $c$ possible names in Korean lexicographic order, one per line.

• $1 \leq T \leq 20$.
• $1 \leq n \leq m \leq k \leq 200\,000$.
• The sum of $m$ over all test cases does not exceed $200\,000$.
• The sum of $k$ over all test cases does not exceed $200\,000$.
• Every name consists of between $2$ and $10$ precomposed Hangul syllables.
• $b_i \neq b_j$ ($1 \leq i < j \leq k$).
• Every name among $a_1,a_2,\cdots,a_{m-1}$ appears among $b_1,b_2,\cdots,b_k$.
• $a_1<a_2<\cdots<a_{m-1}$ and $b_1<b_2<\cdots<b_k$.
• At least one possible name exists in every test case.