CF1689A.Lex String

Kuznecov likes art, poetry, and music. And strings consisting of lowercase English letters.

Recently, Kuznecov has found two strings, $a$ and $b$ , of lengths $n$ and $m$ respectively. They consist of lowercase English letters and no character is contained in both strings.

Let another string $c$ be initially empty. Kuznecov can do the following two types of operations:

• Choose any character from the string $a$ , remove it from $a$ , and add it to the end of $c$ .
• Choose any character from the string $b$ , remove it from $b$ , and add it to the end of $c$ .

But, he can not do more than $k$ operations of the same type in a row. He must perform operations until either $a$ or $b$ becomes empty. What is the lexicographically smallest possible value of $c$ after he finishes?

A string $x$ is lexicographically smaller than a string $y$ if and only if one of the following holds:

• $x$ is a prefix of $y$ , but $x \neq y$ ;
• in the first position where $x$ and $y$ differ, the string $x$ has a letter that appears earlier in the alphabet than the corresponding letter in $y$ .

There are several test cases in the input data. The first line contains a single integer $t$ ( $1 \leq t \leq 100$ ) — the number of test cases. This is followed by the test cases description.

The first line of each test case contains three integers $n$ , $m$ , and $k$ ( $1\leq n,m,k \leq 100$ ) — parameters from the statement.

The second line of each test case contains the string $a$ of length $n$ .

The third line of each test case contains the string $b$ of length $m$ .

The strings contain only lowercase English letters. It is guaranteed that no symbol appears in $a$ and $b$ simultaneously.

In each test case, output a single string $c$ — the answer to the problem.

In the first test case, it is optimal to take two 'a's from the string $a$ and add them to the string $c$ . Then it is forbidden to take more characters from $a$ , hence one character 'b' from the string $b$ has to be taken. Following that logic, we end up with $c$ being 'aabaabaa' when string $a$ is emptied.

In the second test case it is optimal to take as many 'a's from string $a$ as possible, then take as many 'b's as possible from string $b$ . In the end, we take two 'c's from the string $a$ emptying it.