#include <bits/stdc++.h>
using namespace std;
int main(void) {
  int test_case;
  cin >> test_case;
  for (int t = 0; t < test_case; t++) {
    int n, a, b;
    vector<int> arr;
    cin >> n >> a >> b;
    if ((a + b + 2 > n) || (abs(a - b) > 1)) {
      cout << -1 << endl;
      continue;
    }
    for (int i = 1; i <= n; i++) arr.push_back(i);
    if (b > a) {
      int idx = 2;
      for (int i = 0; i < a; i++) {
        swap(arr[idx], arr[idx + 1]);
        idx += 2;
      }
      swap(arr[0], arr[1]);
    } else if (b == a) {
      int idx = 1;
      for (int i = 0; i < a; i++) {
        swap(arr[idx], arr[idx + 1]);
        idx += 2;
      }
    } else {
      int idx = 1;
      for (int i = 0; i < b; i++) {
        swap(arr[idx], arr[idx + 1]);
        idx += 2;
      }
      swap(arr[n - 2], arr[n - 1]);
    }
    for (int i : arr) cout << i << " ";
    cout << endl;
  }
}

### 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>
using namespace std;
int main(void) {
  int test_case;
  cin >> test_case;
  for (int t = 0; t < test_case; t++) {
    int n, a, b;
    vector<int> arr;
    cin >> n >> a >> b;
    if ((a + b + 2 > n) || (abs(a - b) > 1)) {
      cout << -1 << endl;
      continue;
    }
    for (int i = 1; i <= n; i++) arr.push_back(i);
    if (b > a) {
      int idx = 2;
      for (int i = 0; i < a; i++) {
        swap(arr[idx], arr[idx + 1]);
        idx += 2;
      }
      swap(arr[0], arr[1]);
    } else if (b == a) {
      int idx = 1;
      for (int i = 0; i < a; i++) {
        swap(arr[idx], arr[idx + 1]);
        idx += 2;
      }
    } else {
      int idx = 1;
      for (int i = 0; i < b; i++) {
        swap(arr[idx], arr[idx + 1]);
        idx += 2;
      }
      swap(arr[n - 2], arr[n - 1]);
    }
    for (int i : arr) cout << i << " ";
    cout << endl;
  }
}

```