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...":



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Can you provide a Python code to find the x-th lexicographically smallest of them?
assistant
#Here is Python code to find the x-th lexicographically smallest of them.
 
def main():
    
    t = int(input())
    allans = []
    for _ in range(t):
        n, k, x = readIntArr()
        x -= 1
        s = input()
        cnts = 0
        arr = [] # store a or how many bs there can be in this place
        for i, c in enumerate(s):
            if c == 'a':
                if cnts > 0:
                    arr.append(cnts * k)
                    cnts = 0
                arr.append(c)
            else: # asterisk
                cnts += 1
        if cnts > 0:
            arr.append(cnts * k)
        numIdxes = [] # numerical indexes
        cntsAtIdxes = []
        for i, c in enumerate(arr):
            if type(c) == int:
                numIdxes.append(i)
                cntsAtIdxes.append(c)
        m = len(numIdxes)
        suffixProducts = [1] * m # exclude itself
        for i in range(m - 2, -1, -1):
            suffixProducts[i] = suffixProducts[i + 1] * (cntsAtIdxes[i + 1] + 1)
        # every 1 at numIdxes[i] will increase ans by suffixProducts[i]
        
        requiredCnts = [0] * m
        for i in range(m):
            j = x // suffixProducts[i]
            requiredCnts[i] = j
            x -= j * suffixProducts[i]
        ans = []
        j = 0
        for c in arr:
            if c == 'a':
                ans.append('a')
            else:
                for __ in range(requiredCnts[j]):
                    ans.append('b')
                j += 1
        allans.append(''.join(ans))
        
    multiLineArrayPrint(allans)
    
    return

import sys
# input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)
input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS.

def oneLineArrayPrint(arr):
    print(' '.join([str(x) for x in arr]))
def multiLineArrayPrint(arr):
    print('\n'.join([str(x) for x in arr]))
def multiLineArrayOfArraysPrint(arr):
    print('\n'.join([' '.join([str(x) for x in y]) for y in arr]))
 
def readIntArr():
    return [int(x) for x in input().split()]
# def readFloatArr():
#     return...