#include <bits/stdc++.h>
using namespace std;
void _print(long long t) { cerr << t; }
void _print(int t) { cerr << t; }
void _print(string t) { cerr << t; }
void _print(char t) { cerr << t; }
void _print(long double t) { cerr << t; }
void _print(double t) { cerr << t; }
void _print(unsigned long long t) { cerr << t; }
template <class T, class V>
void _print(pair<T, V> p);
template <class T>
void _print(vector<T> v);
template <class T>
void _print(set<T> v);
template <class T, class V>
void _print(map<T, V> v);
template <class T>
void _print(multiset<T> v);
template <class T, class V>
void _print(pair<T, V> p) {
  cerr << "{";
  _print(p.first);
  cerr << ",";
  _print(p.second);
  cerr << "}";
}
template <class T>
void _print(vector<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(set<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(multiset<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T, class V>
void _print(map<T, V> v) {
  cerr << "[ ";
  for (auto i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int tc = 1;
  cin >> tc;
  while (tc--) {
    long long n, k, x;
    cin >> n >> k >> x;
    string second;
    cin >> second;
    vector<int> astericks;
    int cnt = 0;
    for (int i = n - 1; i >= 0; i--) {
      if (second[i] == '*') {
        cnt += k;
        if (i == 0) astericks.push_back(cnt);
      } else if (second[i] == 'a') {
        if (cnt) astericks.push_back(cnt);
        cnt = 0;
      }
    }
    if (x == 1) {
      for (int i = 0; i < n; i++)
        if (second[i] == 'a') cout << second[i];
      cout << "\n";
      continue;
    }
    vector<long long> dp(astericks.size(), LLONG_MAX);
    dp[0] = astericks[0] + 1;
    for (int i = 1; i < dp.size(); i++) {
      if (x / (astericks[i] + 1) < dp[i - 1]) break;
      dp[i] = (astericks[i] + 1) * dp[i - 1];
    }
    reverse(astericks.begin(), astericks.end());
    reverse(dp.begin(), dp.end());
    vector<int> ch(astericks.size());
    bool st = 0;
    for (int i = 0; i < ch.size(); i++) {
      if (x == dp[i]) {
        x = 0;
        for (int j = i; j < ch.size(); j++) ch[j] = astericks[j];
        break;
      } else if (x > dp[i]) {
        while (x > dp[i]) x -= dp[i], ch[i - 1]++;
        i--;
      } else if (i == ch.size() - 1)
        ch[ch.size() - 1] = x - 1;
    }
    int idx = 0;
    for (int i = 0; i < n; i++) {
      if (second[i] == '*') {
        while (i < n && second[i] == '*') i++;
        i--;
        if (idx >= ch.size()) {
          cout << n << k << x << second << "\n";
          break;
        }
        for (int j = 0; j < ch[idx]; j++) cout << (char)('b');
        idx++;
      } else
        cout << (char)('a');
    }
    cout << "\n";
  }
}

### Prompt

Create a solution in cpp for 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;
void _print(long long t) { cerr << t; }
void _print(int t) { cerr << t; }
void _print(string t) { cerr << t; }
void _print(char t) { cerr << t; }
void _print(long double t) { cerr << t; }
void _print(double t) { cerr << t; }
void _print(unsigned long long t) { cerr << t; }
template <class T, class V>
void _print(pair<T, V> p);
template <class T>
void _print(vector<T> v);
template <class T>
void _print(set<T> v);
template <class T, class V>
void _print(map<T, V> v);
template <class T>
void _print(multiset<T> v);
template <class T, class V>
void _print(pair<T, V> p) {
  cerr << "{";
  _print(p.first);
  cerr << ",";
  _print(p.second);
  cerr << "}";
}
template <class T>
void _print(vector<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(set<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(multiset<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T, class V>
void _print(map<T, V> v) {
  cerr << "[ ";
  for (auto i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int tc = 1;
  cin >> tc;
  while (tc--) {
    long long n, k, x;
    cin >> n >> k >> x;
    string second;
    cin >> second;
    vector<int> astericks;
    int cnt = 0;
    for (int i = n - 1; i >= 0; i--) {
      if (second[i] == '*') {
        cnt += k;
        if (i == 0) astericks.push_back(cnt);
      } else if (second[i] == 'a') {
        if (cnt) astericks.push_back(cnt);
        cnt = 0;
      }
    }
    if (x == 1) {
      for (int i = 0; i < n; i++)
        if (second[i] == 'a') cout << second[i];
      cout << "\n";
      continue;
    }
    vector<long long> dp(astericks.size(), LLONG_MAX);
    dp[0] = astericks[0] + 1;
    for (int i = 1; i < dp.size(); i++) {
      if (x / (astericks[i] + 1) < dp[i - 1]) break;
      dp[i] = (astericks[i] + 1) * dp[i - 1];
    }
    reverse(astericks.begin(), astericks.end());
    reverse(dp.begin(), dp.end());
    vector<int> ch(astericks.size());
    bool st = 0;
    for (int i = 0; i < ch.size(); i++) {
      if (x == dp[i]) {
        x = 0;
        for (int j = i; j < ch.size(); j++) ch[j] = astericks[j];
        break;
      } else if (x > dp[i]) {
        while (x > dp[i]) x -= dp[i], ch[i - 1]++;
        i--;
      } else if (i == ch.size() - 1)
        ch[ch.size() - 1] = x - 1;
    }
    int idx = 0;
    for (int i = 0; i < n; i++) {
      if (second[i] == '*') {
        while (i < n && second[i] == '*') i++;
        i--;
        if (idx >= ch.size()) {
          cout << n << k << x << second << "\n";
          break;
        }
        for (int j = 0; j < ch[idx]; j++) cout << (char)('b');
        idx++;
      } else
        cout << (char)('a');
    }
    cout << "\n";
  }
}

```