#include <bits/stdc++.h>
using namespace std;
int i, j, m, n, s, t, x, z, y;
int main() {
  cin >> n;
  while (n--) {
    cin >> x >> y >> z;
    if (y + z >= x - 1 || y - z > 1 || y - z < -1) {
      cout << -1 << endl;
      continue;
    }
    if (y > z) {
      cout << x - 1;
      for (i = 1; i <= y; i++) {
        cout << " " << x - (2 * i - 2);
        if (i != y)
          cout << " " << x - (2 * i + 1);
        else
          cout << " " << x - (2 * i);
      }
      for (i = x - (2 * y + 1); i >= 1; i--) cout << " " << i;
      cout << endl;
    }
    if (y < z) {
      cout << 2;
      for (i = 1; i <= y; i++) {
        cout << " " << 2 * i - 1;
        cout << " " << 2 * i + 2;
      }
      cout << " " << 2 * y + 2 - 1;
      for (i = 2 * y + 2 + 1; i <= x; i++) cout << " " << i;
    }
    if (y == z) {
      cout << 1;
      for (i = 1; i <= y; i++) {
        cout << " " << 2 * i + 1;
        cout << " " << 2 * i;
      }
      for (i = 2 * y + 2; i <= x; i++) cout << " " << i;
    }
    cout << endl;
  }
}

### Prompt

Please provide a CPP coded solution 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;
int i, j, m, n, s, t, x, z, y;
int main() {
  cin >> n;
  while (n--) {
    cin >> x >> y >> z;
    if (y + z >= x - 1 || y - z > 1 || y - z < -1) {
      cout << -1 << endl;
      continue;
    }
    if (y > z) {
      cout << x - 1;
      for (i = 1; i <= y; i++) {
        cout << " " << x - (2 * i - 2);
        if (i != y)
          cout << " " << x - (2 * i + 1);
        else
          cout << " " << x - (2 * i);
      }
      for (i = x - (2 * y + 1); i >= 1; i--) cout << " " << i;
      cout << endl;
    }
    if (y < z) {
      cout << 2;
      for (i = 1; i <= y; i++) {
        cout << " " << 2 * i - 1;
        cout << " " << 2 * i + 2;
      }
      cout << " " << 2 * y + 2 - 1;
      for (i = 2 * y + 2 + 1; i <= x; i++) cout << " " << i;
    }
    if (y == z) {
      cout << 1;
      for (i = 1; i <= y; i++) {
        cout << " " << 2 * i + 1;
        cout << " " << 2 * i;
      }
      for (i = 2 * y + 2; i <= x; i++) cout << " " << i;
    }
    cout << endl;
  }
}

```