#P1925A. We Got Everything Covered!
We Got Everything Covered!
Description
You are given two positive integers $n$ and $k$.
Your task is to find a string $s$ such that all possible strings of length $n$ that can be formed using the first $k$ lowercase English alphabets occur as a subsequence of $s$.
If there are multiple answers, print the one with the smallest length. If there are still multiple answers, you may print any of them.
Note: A string $a$ is called a subsequence of another string $b$ if $a$ can be obtained by deleting some (possibly zero) characters from $b$ without changing the order of the remaining characters.
The first line of input contains a single integer $t$ ($1\leq t\leq 676$) denoting the number of test cases.
Each test case consists of a single line of input containing two integers $n$ ($1\leq n\leq 26$) and $k$ ($1\leq k\leq 26$).
For each test case, print a single line containing a single string $s$ which satisfies the above property. If there are multiple answers, print the one with the smallest length. If there are still multiple answers, you may print any of them.
Input
The first line of input contains a single integer $t$ ($1\leq t\leq 676$) denoting the number of test cases.
Each test case consists of a single line of input containing two integers $n$ ($1\leq n\leq 26$) and $k$ ($1\leq k\leq 26$).
Output
For each test case, print a single line containing a single string $s$ which satisfies the above property. If there are multiple answers, print the one with the smallest length. If there are still multiple answers, you may print any of them.
4
1 2
2 1
2 2
2 3
ab
aa
baab
abcbac
Note
For the first test case, there are two strings of length $1$ which can be formed using the first $2$ lowercase English alphabets, and they are present in $s$ as a subsequence as follows:
- $\texttt{a}: {\color{red}{\texttt{a}}}\texttt{b}$
- $\texttt{b}: \texttt{a}{\color{red}{\texttt{b}}}$
For the second test case, there is only one string of length $2$ which can be formed using the first lowercase English alphabet, and it is present in $s$ as a subsequence as follows:
- $\texttt{aa}: {\color{red}{\texttt{aa}}}$
For the third test case, there are $4$ strings of length $2$ which can be formed using the first $2$ lowercase English alphabets, and they are present in $s$ as a subsequence as follows:
- $\texttt{aa}: \texttt{b}{\color{red}{\texttt{aa}}}\texttt{b}$
- $\texttt{ab}: \texttt{ba}{\color{red}{\texttt{ab}}}$
- $\texttt{ba}: {\color{red}{\texttt{ba}}}\texttt{ab}$
- $\texttt{bb}: {\color{red}{\texttt{b}}}\texttt{aa}{\color{red}{\texttt{b}}}$
For the fourth test case, there are $9$ strings of length $2$ which can be formed using the first $3$ lowercase English alphabets, and they are present in $s$ as a subsequence as follows:
- $\texttt{aa}: {\color{red}{\texttt{a}}}\texttt{bcb}{\color{red}{\texttt{a}}}\texttt{c}$
- $\texttt{ab}: {\color{red}{\texttt{ab}}}\texttt{cbac}$
- $\texttt{ac}: \texttt{abcb}{\color{red}{\texttt{ac}}}$
- $\texttt{ba}: \texttt{abc}{\color{red}{\texttt{ba}}}\texttt{c}$
- $\texttt{bb}: \texttt{a}{\color{red}{\texttt{b}}}\texttt{c}{\color{red}{\texttt{b}}}\texttt{ac}$
- $\texttt{bc}: \texttt{a}{\color{red}{\texttt{bc}}}\texttt{bac}$
- $\texttt{ca}: \texttt{ab}{\color{red}{\texttt{c}}}\texttt{b}{\color{red}{\texttt{a}}}\texttt{c}$
- $\texttt{cb}: \texttt{ab}{\color{red}{\texttt{cb}}}\texttt{ac}$
- $\texttt{cc}: \texttt{ab}{\color{red}{\texttt{c}}}\texttt{ba}{\color{red}{\texttt{c}}}$