#include <bits/stdc++.h>
using namespace std;
const int mod = 100000007;
const int mini = -2147483648;
const int maxi = 2147483647;
void _print(long long 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 << "]";
}
void solve() {
  long long int n, a, b;
  cin >> n >> a >> b;
  vector<long long int> v(n);
  if ((a + b) > (n - 2) || abs(a - b) > 1) {
    cout << -1;
    return;
  }
  for (long long int i = 0; i < n; i++) {
    v[i] = i + 1;
  }
  long long int maxx = max(a, b);
  if (a == b) {
    long long int cnt = 0;
    for (long long int i = 1; i < n - 1; i++) {
      if (cnt == a) break;
      swap(v[i], v[i + 1]);
      cnt++;
      i++;
    }
  } else {
    long long int cnt = 0;
    for (long long int i = 0; i < n; i++) {
      if (maxx > cnt) {
        swap(v[i], v[i + 1]);
        cnt++;
        i++;
      } else
        break;
    }
    if (maxx == a) {
      for (long long int i = 0; i < n; i++) {
        v[i] = n - v[i] + 1;
      }
    }
  }
  for (auto &i : v) {
    cout << i << " ";
  }
}
signed main() {
  freopen("Error.txt", "w", stderr);
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  auto start = chrono::high_resolution_clock::now();
  long long int t = 1;
  cin >> t;
  while (t--) {
    solve();
    cout << "\n";
  }
  auto stop = chrono::high_resolution_clock::now();
  auto duration = chrono::duration_cast<chrono::microseconds>(stop - start);
  cerr << "\n"
       << "Time : " << duration.count() / 1e3 << " ms\n";
}

### Prompt

In Cpp, your task is to solve the following problem:

You are given three integers n, a, b. Determine if there exists a permutation p_1, p_2, …, p_n of integers from 1 to n, such that:

  * There are exactly a integers i with 2 ≤ i ≤ n-1 such that p_{i-1} < p_i > p_{i+1} (in other words, there are exactly a local maximums).

  * There are exactly b integers i with 2 ≤ i ≤ n-1 such that p_{i-1} > p_i < p_{i+1} (in other words, there are exactly b local minimums).




If such permutations exist, find any such permutation.

Input

The first line of the input contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases. The description of test cases follows.

The only line of each test case contains three integers n, a and b (2 ≤ n ≤ 10^5, 0 ≤ a,b ≤ n).

The sum of n over all test cases doesn't exceed 10^5.

Output

For each test case, if there is no permutation with the requested properties, output -1.

Otherwise, print the permutation that you are found. If there are several such permutations, you may print any of them.

Example

Input


3
4 1 1
6 1 2
6 4 0


Output


1 3 2 4
4 2 3 1 5 6
-1

Note

In the first test case, one example of such permutations is [1, 3, 2, 4]. In it p_1 < p_2 > p_3, and 2 is the only such index, and p_2> p_3 < p_4, and 3 the only such index.

One can show that there is no such permutation for the third test case.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int mod = 100000007;
const int mini = -2147483648;
const int maxi = 2147483647;
void _print(long long 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 << "]";
}
void solve() {
  long long int n, a, b;
  cin >> n >> a >> b;
  vector<long long int> v(n);
  if ((a + b) > (n - 2) || abs(a - b) > 1) {
    cout << -1;
    return;
  }
  for (long long int i = 0; i < n; i++) {
    v[i] = i + 1;
  }
  long long int maxx = max(a, b);
  if (a == b) {
    long long int cnt = 0;
    for (long long int i = 1; i < n - 1; i++) {
      if (cnt == a) break;
      swap(v[i], v[i + 1]);
      cnt++;
      i++;
    }
  } else {
    long long int cnt = 0;
    for (long long int i = 0; i < n; i++) {
      if (maxx > cnt) {
        swap(v[i], v[i + 1]);
        cnt++;
        i++;
      } else
        break;
    }
    if (maxx == a) {
      for (long long int i = 0; i < n; i++) {
        v[i] = n - v[i] + 1;
      }
    }
  }
  for (auto &i : v) {
    cout << i << " ";
  }
}
signed main() {
  freopen("Error.txt", "w", stderr);
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  auto start = chrono::high_resolution_clock::now();
  long long int t = 1;
  cin >> t;
  while (t--) {
    solve();
    cout << "\n";
  }
  auto stop = chrono::high_resolution_clock::now();
  auto duration = chrono::duration_cast<chrono::microseconds>(stop - start);
  cerr << "\n"
       << "Time : " << duration.count() / 1e3 << " ms\n";
}

```