human
Can you provide a Python program to find the x-th lexicographically smallest of them given the following:
PYTHON3 solution for "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 ≠ 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 ≠ 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.

Input

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

The first line of each testcase contains three integers n, k and x (1 ≤ n ≤ 2000.
0 ≤ k ≤ 2000.
1 ≤ x ≤ 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'.

Output

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

Example

Input

3
2 4 3
a*
4 1 3
a**a
6 3 20
**a***

Output

abb
abba
babbbbbbbbb

Note

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...":
assistant
#Here is Python program to find the x-th lexicographically smallest of them.
 def solver():
    n_1 = int(input())

    for _ in range(n_1):
        n, k, x = map(int, input().split())
        f = input()
        a = list(filter(lambda y: y != "", f.split("a")))

        list_of_cases = []
        tmp = ""
        for i in f:
            if i == "a":
                list_of_cases.append(tmp)
                tmp = ""
                list_of_cases.append("a")
            else:
                tmp = tmp + "*"
        list_of_cases.append(tmp)
        list_of_cases = list(filter(lambda y: y != "", list_of_cases))

        n_of_cases = 1
        for multiplier in a:
            n_of_cases = n_of_cases * (len(multiplier)*k + 1)
        final = ""

        for i in list_of_cases:
            if i == "a":
                final = final + "a"
            else:
                length = len(i)
                chunks = length * k + 1
                n_of_cases = n_of_cases // chunks
                for j in range(chunks):
                    if j * n_of_cases < x <= (j+1) * n_of_cases:
                        final = final + j*"b"
                        x = x % n_of_cases
                        if x == 0:
                            x = n_of_cases

        print(final)

solver()