human
Can you solve the below in PYTHON3?
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.

import sys
from random import randint
input = lambda : sys.stdin.readline().strip()
intput = lambda : map(int, input().split())

def toStr(new, res):
    a = []
    n = len(new)
    c = 0
    for i in range(n):
        if new[i] == 'a':
            a.append('a')
        else:
            a.append('b' * res[c])
            c += 1
    # print(a)
    return "".join(a)

def solve(k,x,s):
    s += "$"
    stk = 0
    new = []
    for i, ch in enumerate(s):
        if ch == '*': stk += 1
        else:
            if i != 0 and s[i-1] != 'a':
                new.append(stk)
                stk = 0
        if ch == 'a':
            new.append('a')
    q = [y for y in new if y != 'a']
    if not q: return s[:-1]
    n = len(q)
    for i in range(n):
        q[i] = q[i] * k + 1
    for i in range(n-2, -1, -1):
        q[i] *= q[i+1]
    x -= 1

    for i in range(n-1, -1, -1):
        if q[i] > x: break

    res = [0] * n
    if i == n-1:
        res[i] = x
        return toStr(new, res)

    while i < n-1:
        b = x // q[i+1]
        x %= q[i+1]
        res[i] = b
        i += 1
    res[-1] = x
    # print(new, res)
    return toStr(new, res)

def random():
    b = []
    for i in range(randint(0,50)):
        a = randint(0,1)
        x = randint(0,20)
        if a == 0:
            b.append(x * '*')
        else:
            b.append(x * 'a')
    return ''.join(b)

def test(x, k, s):
    A = set()
    def dfs(i, curr):
        if i >= len(s):
            A.add(str(curr))
            return
        if s[i] == '*':
            for j in range(k+1):
                q = curr + 'b'*j
                dfs(i+1, q)
        else: dfs(i+1, curr + 'a')
    dfs(0, "")
    return sorted(A)[x-1]

if __name__ == '__main__':
    # print( test(319, 3, '**a***aa*aa*') )
    # print( test(20, 3, '**a***'))

    T, = intput()
    for _ in range(T):
        n, k, x = intput()
        s = input()
        print( solve(k,x,s) )
        # s = random()
        # k = randint(0,10)
        # x = (randint(0,20))
        #...