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 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 fun(arr, x):
    y = 1
    i = 0
    while y < x:
        y *= arr[i]
        i += 1
    i -= 1
    y = y//arr[i]
    z = y
    y = 0
    j = 0
    while y < x:
        y += z
        j += 1
    j-= 1
    return [i,j,y-z]

for _ in range(int(input())):
    n, k, x = map(int,input().split())
    s = input()
    arr = []
    c = 0
    flag = True
    for i in s:
        if i == 'a':
            if flag:
                arr.append(c*k+1)
                c = 0
                flag = False
        else:
            c += 1
            flag = True
    if flag:
        arr.append(c*k+1)
    if s[0] == 'a':
        arr.pop(0)
    arr = arr[::-1]
    ans = [0]*len(arr)
    sol = ''
    while x > 1:
        coord = fun(arr, x)
        i, j = coord[0], coord[1]
        # print(coord)
        x -= coord[2]
        # print(x)
        ans[i] = j
    ans = ans[::-1]

    flag = True
    j = 0
    for i in s:
        if i == 'a':
            sol += 'a'
            flag = True
        else:
            if flag:
                sol += 'b'*ans[j]
                j += 1
                flag = False
    if sol == '':
        print('b')
    else:
        print(sol)