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...":


 Write 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 solve():
    [N, K, X] = [int(x) for x in input().split()]
    SS = list(input())
    if SS.count('a')==len(SS):
        print(''.join(SS))
        return 
    S = list(reversed(SS))
    sp = [0]
    for i in range(len(S)):
        if S[i]=='*':
            sp[-1]+=1
        else:
            if sp[-1]!=0:
                sp.append(0)
    if sp[-1]==0: sp.pop()
    cur = 0
    p = sp[0]*K+1
    pot = [p]
    sol = [0]
    while p<X:
        cur+=1
        p*=sp[cur]*K+1
        pot.append(p)
        sol.append(0)
    X-=1
    for i in range(cur, 0, -1):
        sol[i] = X // pot[i-1]
        X %= pot[i-1]    
    sol[0] = X
    sol = sol + [0]*(len(sp)-cur-1)
    SSS = []
    cur = len(sol)-1
    for i in range(len(SS)):
        if SS[i]=='a': SSS.append('a')
        elif SS[i]=='*' and (i==0 or SS[i-1]!='*'):
            SSS.append('b'*sol[cur])
            cur-=1
    print(''.join(SSS))
    
T = int(input())
for i in range(T):
    solve()