human
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...":


 Give me a Python program to find the x-th lexicographically smallest of them?
assistant
#Here is Python program to find the x-th lexicographically smallest of them.
 def solution(n, k, x, s):
    current_len = 0
    astrics = []
    for c in s:
        if   c == '*':
            current_len += 1
        elif c == 'a':
            if current_len != 0:
                astrics.append(current_len)
            current_len = 0
    if current_len != 0:
        astrics.append(current_len)
    astrics = list(map(lambda y: k*y+1, astrics))
    x -= 1
    result = []
    for num in reversed(astrics):
        m = x % num
        x //= num
        result.append(m)

    answer = ''
    c = s[0]
    if c == 'a':
        answer = 'a'
    for i in range(1, n):
        if s[i] == 'a' and s[i - 1] == '*':
            num = result.pop()
            answer += num * 'b'
        if s[i] == 'a':
            answer += 'a'
    if s[n - 1] == '*':
        num = result.pop()
        answer += num * 'b'

    return answer

if __name__ == '__main__':
    t = int(input())
    for i in range(t):
        n, k, x = list(map(int, input().split()))
        s = input()
        print(solution(n, k, x, s))