#include <bits/stdc++.h>
using namespace std;
void solve();
int main() {
  int t = 1;
  while (t--) {
    solve();
    cout << endl;
  }
  return 0;
}
void solve() {
  int n, a, b;
  cin >> n >> a >> b;
  if (abs(a - b) <= 1 && a + b + 2 <= n) {
    if (a <= b) {
      int i, j, k = min(a, b);
      if (a < b) {
        cout << 2 << " " << 1 << " ";
        i = 4, j = 3;
      } else {
        cout << 1 << " ";
        i = 3, j = 2;
      }
      for (; max(i, j) < n && k > 0; i += 2, j += 2, k--)
        cout << i << " " << j << " ";
      for (int t = min(i, j); t <= n; t++) cout << t << " ";
    } else {
      int i = n - 1, j = n, k = max(a, b);
      for (; min(i, j) > 0 && k > 0; i -= 2, j -= 2, k--)
        cout << i << " " << j << " ";
      for (int t = max(i, j); t > 0; t--) cout << t << " ";
    }
  } else {
    cout << -1;
  }
}

### 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;
void solve();
int main() {
  int t = 1;
  while (t--) {
    solve();
    cout << endl;
  }
  return 0;
}
void solve() {
  int n, a, b;
  cin >> n >> a >> b;
  if (abs(a - b) <= 1 && a + b + 2 <= n) {
    if (a <= b) {
      int i, j, k = min(a, b);
      if (a < b) {
        cout << 2 << " " << 1 << " ";
        i = 4, j = 3;
      } else {
        cout << 1 << " ";
        i = 3, j = 2;
      }
      for (; max(i, j) < n && k > 0; i += 2, j += 2, k--)
        cout << i << " " << j << " ";
      for (int t = min(i, j); t <= n; t++) cout << t << " ";
    } else {
      int i = n - 1, j = n, k = max(a, b);
      for (; min(i, j) > 0 && k > 0; i -= 2, j -= 2, k--)
        cout << i << " " << j << " ";
      for (int t = max(i, j); t > 0; t--) cout << t << " ";
    }
  } else {
    cout << -1;
  }
}

```