C. BA-Stringtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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'.OutputFor each testcase, print a single string, consisting only of characters 'b' and 'a' (lowercase Latin letters) — the x-th lexicographically smallest BA-string.ExampleInput
3
2 4 3
a*
4 1 3
a**a
6 3 20
**a***
Output
abb
abba
babbbbbbbbb
NoteIn the first testcase of the example, BA-strings ordered lexicographically are:   a  ab  abb  abbb  abbbb In the second testcase of the example, BA-strings ordered lexicographically are:   aa  aba  abba Note that string "aba" is only counted once, even though there are two ways to replace asterisks with characters 'b' to get it.
3
2 4 3
a*
4 1 3
a**a
6 3 20
**a***

abb abba babbbbbbbbb 
['brute force', 'dp', 'greedy', 'implementation', 'math', '*1800']