#include <bits/stdc++.h>
using namespace std;
const int MAXN = 2001;
char s[MAXN];
long long a[MAXN];
int b[MAXN];
int main() {
  int tn, n, k, m;
  long long x;
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  scanf("%d", &tn);
  while (tn--) {
    scanf("%d%d%lld%s", &n, &k, &x, s);
    --x;
    m = 0;
    memset(a, 0, sizeof(long long) * n);
    memset(b, 0, sizeof(int) * n);
    for (int i = 0; i < n; ++i)
      if (i > 0 && s[i] == s[i - 1] && s[i] == '*')
        a[m - 1] += k;
      else
        a[m++] = (s[i] == '*' ? k + 1 : 0);
    for (int i = m - 1; i >= 0; --i)
      if (a[i] > 0) b[i] = x % a[i], x /= a[i];
    for (int i = 0; i < m; ++i)
      if (a[i] == 0)
        printf("a");
      else
        for (int j = 0; j < b[i]; ++j) printf("b");
    printf("\n");
  }
  return 0;
}

### Prompt

Please create a solution in cpp to the following problem:

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 'b' to get it.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 2001;
char s[MAXN];
long long a[MAXN];
int b[MAXN];
int main() {
  int tn, n, k, m;
  long long x;
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  scanf("%d", &tn);
  while (tn--) {
    scanf("%d%d%lld%s", &n, &k, &x, s);
    --x;
    m = 0;
    memset(a, 0, sizeof(long long) * n);
    memset(b, 0, sizeof(int) * n);
    for (int i = 0; i < n; ++i)
      if (i > 0 && s[i] == s[i - 1] && s[i] == '*')
        a[m - 1] += k;
      else
        a[m++] = (s[i] == '*' ? k + 1 : 0);
    for (int i = m - 1; i >= 0; --i)
      if (a[i] > 0) b[i] = x % a[i], x /= a[i];
    for (int i = 0; i < m; ++i)
      if (a[i] == 0)
        printf("a");
      else
        for (int j = 0; j < b[i]; ++j) printf("b");
    printf("\n");
  }
  return 0;
}

```