Passwords

Ahmed administers the contest system and generated one login password per team, then lost the list of passwords. He still remembers how he built them.

Ahmed keeps a list $X$ of $N$ strings. A list $P$ is a permutation of $X$ when $P$ holds exactly the same elements as $X$, possibly in a different order. He builds every permutation of $X$. For each permutation $P$ he concatenates the strings of $P$ from front to back into a single string, and he gathers all of those strings into a list $Y$. Finally he sorts $Y$ lexicographically according to the ASCII table and deletes duplicate strings. The passwords are the strings at predetermined positions of that cleaned-up $Y$.

Given the list $X$ and a position $K$, print the $K$-th password in $Y$. Positions are counted from 1.

The first line contains an integer $T$, the number of test cases.

Each test case starts with the size $N$ ($N \le 20$) of the list $X$ and the position $K$, followed by $N$ strings. Each string is at most 10 characters long, and all $N$ strings have the same length. The strings contain no whitespace and consist only of upper and lower case letters. $K$ is always a valid position.

For each test case, print the $K$-th password on its own line.