A14857. BA-String

You are given an integer $k$ and a string $s$ that consists only of characters 'a' (a lowercase Latin letter) and '\*' (an asterisk).

Each asterisk should be replaced with several (from $0$ to $k$ inclusive) lowercase Latin letters 'b'. Different asterisk can be replaced with different counts of letter 'b'.

The result of the replacement is called a BA-string.

Two strings $a$ and $b$ are different if they either have different lengths or there exists such a position $i$ that $a_i \neq b_i$ .

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

- $a$ is a prefix of $b$ , but $a \ne b$ ;
- in the first position where $a$ and $b$ differ, the string $a$ has a letter that appears earlier in the alphabet than the corresponding letter in $b$ .

Now consider all different BA-strings and find the $x$ -th lexicographically smallest of them.

The first line contains a single integer $t$ ( $1 \le t \le 2000$ ) — the number of testcases.

The first line of each testcase contains three integers $n$ , $k$ and $x$ ( $1 \le n \le 2000$ ; $0 \le k \le 2000$ ; $1 \le x \le 10^{18}$ ). $n$ is the length of string $s$ .

The second line of each testcase is a string $s$ . It consists of $n$ characters, each of them is either 'a' (a lowercase Latin letter) or '\*' (an asterisk).

The sum of $n$ over all testcases doesn't exceed $2000$ . For each testcase $x$ doesn't exceed the total number of different BA-strings. String $s$ contains at least one character 'a'.

For each testcase, print a single string, consisting only of characters 'b' and 'a' (lowercase Latin letters) — the $x$ -th lexicographically smallest BA-string.

In the first testcase of the example, BA-strings ordered lexicographically are:

1. a
2. ab
3. abb
4. abbb
5. abbbb

In the second testcase of the example, BA-strings ordered lexicographically are:

1. aa
2. aba
3. abba

Note that string "aba" is only counted once, even though there are two ways to replace asterisks with characters 'b' to get it.