human
Give me a Python code 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 code to find the x-th lexicographically smallest of them.
 def main():
    n, k, x = map(int, input().split())
    s = input()
    
    if len(set(s)) == 1:
        return s 
    
    arr = []
    curr = 0
    for i in range(n):
        if s[i] == '*':
            curr += 1 
        if s[i] == 'a' and curr > 0:
            arr.append(k*curr+1)
            curr = 0
        
    if curr > 0:
        arr.append(k*curr+1)
    # print(arr)
    l = len(arr)
        
    aux = [0]*l
    c = s[0]
    for i in range(1, n):
        if s[i] == '*' and c[-1] != '*':
            c += '*'
        elif s[i] == 'a':
            c += 'a'
      
    # print(c)
    prod = 1 
    
    arr = arr[::-1]
    
    for i in range(l):
        prod = arr[i]*prod 
        # print('yo')
        
        if prod >= x:
            break
        
    extra = arr[:i+1]
    extra = extra[::-1]
    lol = []
    # print(extra)
    for j in range(i+1):
        prod = prod//extra[j]
        
        a = (x-1)//prod
        lol.append(a)
        x -= a*prod
        
    final = [0]*(l-(i+1)) + lol      
    # arr = arr[::-1]
    # blah = []
    # x -= 1 
    # for j in arr:
    #     blah.append(x % j)
    #     x == x // j 
        
    ans = ''
    i = 0
    
    for k in c:
        if k == 'a':
            ans += 'a'
        else:
            for j in range(final[i]):
                ans += 'b'
            i += 1     
            
        
    
    # print(arr)
    return ans 
    
for _ in range(int(input())):
    print(main())