#include <bits/stdc++.h>
const int xsz = 60 + 1;
const int MOD = 1e9 + 7;
const long long oo = 1e18 + 5;
using namespace std;
void Solve() {
  int n, a, b;
  cin >> n >> a >> b;
  if (abs(a - b) > 1 or a + b > n - 2) {
    cout << "-1\n";
    return;
  }
  int t = 1, rt = n;
  if (a < b) swap(t, rt);
  for (int i = 1; i <= n; ++i) {
    if (i <= a + b + 1) {
      cout << t << " ";
      if (t < rt)
        t++;
      else
        t--;
      swap(t, rt);
    } else {
      cout << rt << " ";
      if (rt < t)
        rt++;
      else
        rt--;
    }
  }
  cout << "\n";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  cin >> t;
  for (int i = 1; i <= t; ++i) {
    Solve();
  }
  return 0;
}

### Prompt

Please create a solution in Cpp to 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>
const int xsz = 60 + 1;
const int MOD = 1e9 + 7;
const long long oo = 1e18 + 5;
using namespace std;
void Solve() {
  int n, a, b;
  cin >> n >> a >> b;
  if (abs(a - b) > 1 or a + b > n - 2) {
    cout << "-1\n";
    return;
  }
  int t = 1, rt = n;
  if (a < b) swap(t, rt);
  for (int i = 1; i <= n; ++i) {
    if (i <= a + b + 1) {
      cout << t << " ";
      if (t < rt)
        t++;
      else
        t--;
      swap(t, rt);
    } else {
      cout << rt << " ";
      if (rt < t)
        rt++;
      else
        rt--;
    }
  }
  cout << "\n";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  cin >> t;
  for (int i = 1; i <= t; ++i) {
    Solve();
  }
  return 0;
}

```