[Solution] Another String Minimization Problem Codeforces Solution

A. Another String Minimization Problem

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You have a sequence a1,a2,…,an$a_1,a_2,\dots ,a_n$ of length n$n$, consisting of integers between 1$1$ and m$m$. You also have a string s$s$, consisting of m$m$ characters B.

You are going to perform the following n$n$ operations.

• At the i$i$-th (1≤i≤n$1\le i\le n$) operation, you replace either the ai$a_i$-th or the (m+1−ai)$(m+1-a_i)$-th character of s$s$ with A. You can replace the character at any position multiple times through the operations.

Find the lexicographically smallest string you can get after these operations.

A string x$x$ is lexicographically smaller than a string y$y$ of the same length if and only if in the first

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 position where x$x$ and y$y$ differ, the string x$x$ has a letter that appears earlier in the alphabet than the corresponding letter in y$y$.

Input

The first line contains the number of test cases t$t$ (1≤t≤2000$1\le t\le 2000$).

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The first line of each test case contains two integers n$n$ and m$m$ (1≤n,m≤50$1\le n,m\le 50$) — the length of the sequence a$a$ and the length of the string s$s$ respectively.

The second line contains n$n$ integers a1,a2,…,an$a_1,a_2,\dots ,a_n$ (1≤ai≤m$1\le a_i\le m$) — the sequence a$a$.

Output

For each test case, print a string of length m$m$ — the lexicographically smallest string you can get. Each character of the string should be either capital English letter A or capital English letter B.