#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000007;
const long long bmod = 1e18 + 7;
void print(int a) { cerr << a; }
void print(double a) { cerr << a; }
void print(long long a) { cerr << a; }
void print(char a) { cerr << a; }
void print(string a) { cerr << a; }
void print(bool a) { cerr << a; }
template <class T, class X>
void print(pair<T, X> p);
template <class T>
void print(vector<T> v);
template <class T>
void print(set<T> v);
template <class T, class X>
void print(map<T, X> v);
template <class T>
void print(multiset<T> v);
template <class T, class X>
void print(pair<T, X> 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 << "]";
  cerr << endl;
}
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>
void print(list<T> v) {
  cerr << "[ ";
  for (T i : v) {
    print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T, class X>
void print(map<T, X> v) {
  cerr << "[ ";
  for (auto i : v) {
    print(i);
    cerr << " ";
  }
  cerr << "]";
}
void solve() {
  int n;
  cin >> n;
  int a, b;
  cin >> a >> b;
  if (a + b > n - 2 || a > (n - 1) / 2 || b > (n - 1) / 2 || abs(a - b) > 1) {
    cout << -1 << endl;
    return;
  }
  int arr[n];
  for (long long i = 0; i < n; i++) {
    arr[i] = i + 1;
  }
  int i = 1;
  if (a == b) {
    while (a > 0 && i < n + 1) {
      swap(arr[i], arr[i + 1]);
      a--;
      i += 2;
    }
  } else if (a > b) {
    i = n - 1;
    while (a > 0 && i < n + 1) {
      swap(arr[i], arr[i - 1]);
      a--;
      i -= 2;
    }
  } else if (b > a) {
    i = 0;
    while (b > 0 && i < n + 1) {
      swap(arr[i], arr[i + 1]);
      b--;
      i += 2;
    }
  }
  for (long long j = 0; j < n; j++) {
    cout << arr[j] << " ";
  }
  cout << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int p = 0;
  freopen("error.txt", "w", stderr);
  int t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
}

### Prompt

Develop a solution in cpp to the problem described below:

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 long long mod = 1000000007;
const long long bmod = 1e18 + 7;
void print(int a) { cerr << a; }
void print(double a) { cerr << a; }
void print(long long a) { cerr << a; }
void print(char a) { cerr << a; }
void print(string a) { cerr << a; }
void print(bool a) { cerr << a; }
template <class T, class X>
void print(pair<T, X> p);
template <class T>
void print(vector<T> v);
template <class T>
void print(set<T> v);
template <class T, class X>
void print(map<T, X> v);
template <class T>
void print(multiset<T> v);
template <class T, class X>
void print(pair<T, X> 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 << "]";
  cerr << endl;
}
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>
void print(list<T> v) {
  cerr << "[ ";
  for (T i : v) {
    print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T, class X>
void print(map<T, X> v) {
  cerr << "[ ";
  for (auto i : v) {
    print(i);
    cerr << " ";
  }
  cerr << "]";
}
void solve() {
  int n;
  cin >> n;
  int a, b;
  cin >> a >> b;
  if (a + b > n - 2 || a > (n - 1) / 2 || b > (n - 1) / 2 || abs(a - b) > 1) {
    cout << -1 << endl;
    return;
  }
  int arr[n];
  for (long long i = 0; i < n; i++) {
    arr[i] = i + 1;
  }
  int i = 1;
  if (a == b) {
    while (a > 0 && i < n + 1) {
      swap(arr[i], arr[i + 1]);
      a--;
      i += 2;
    }
  } else if (a > b) {
    i = n - 1;
    while (a > 0 && i < n + 1) {
      swap(arr[i], arr[i - 1]);
      a--;
      i -= 2;
    }
  } else if (b > a) {
    i = 0;
    while (b > 0 && i < n + 1) {
      swap(arr[i], arr[i + 1]);
      b--;
      i += 2;
    }
  }
  for (long long j = 0; j < n; j++) {
    cout << arr[j] << " ";
  }
  cout << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int p = 0;
  freopen("error.txt", "w", stderr);
  int t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
}

```