Name generator

It is quite difficult to come up with a name for a task in Polygon (a system for preparing tasks). That is why it was necessary to automate this process by developing a name generator.

The name of any task should consist of three parts (listed in order): prefix, separator — symbol "_" (underscore) and suffix. Examples of task names: "amazing_pascal", "clever_einstein", "magical_tesla". Prefix and suffix — words consisting only of lowercase letters of the Latin alphabet, with the prefix chosen only from words in the prefix dictionary and the suffix — in the suffix dictionary.

You have been given $n$ of words in the prefix dictionary and $m$ of words in the suffix dictionary. You have also been given $k$ integers $q_i$ — the numbers of titles to generate. To generate a title numbered $q_i$, you need to find the $q_i$-th title (numbering starts at $1$), among all possible $n\times m$ titles sorted in lexicographic order.

Input

The first line contains three integers $n$, $m$ and $k(1\le n,m,k\le 10^5)$ — respectively the size of the prefix dictionary, the size of the suffix dictionary and the number of names to be generated.

Each of the following $n$ lines contains the string $a_i(1\le |a_i|\le 16)$ — a word from the prefix dictionary consisting of only lowercase letters of the Latin alphabet. It is guaranteed that all words in the prefix dictionary are distinct.

Each of the following $m$ lines contains the string $b_i(1\le |b_i|\le 16)$ — a word from the suffix dictionary consisting of only lowercase letters of the Latin alphabet. It is guaranteed that all words in the suffix dictionary are distinct.

The next line gives $k$ integers $q_i(1\le q_i\le n\cdot m)$ —the numbers of names to be generated.

The entry $|x|$ here denotes the length of the string $x$.

Output

Print $k$ lines. In the $i$-th line print the name of the task under the number $q_i$.

Examples

A string $s$ is lexicographically smaller than a string $t$ if and only if there exists $p$ such that $s_i=t_i$ for $i<p$ and $s_p<t_p$ (or $p>|s|$, $p\le |t|$).

Note: the "_" character is lexicographically smaller than any lowercase letter.