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 $$$y$$$.

Input

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.

Output

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

Note

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.

Idx	Name	Rating
A	Lex String	800
B	Mystic Permutation	900
C	Infected Tree	1600
D	Lena and Matrix	1900
E	ANDfinity	2500

Codeforces Round 798 (Div. 2)