#include <bits/stdc++.h>
using namespace std;
int main() {
  const unsigned int M = 1000000007;
  long long int t;
  cin >> t;
  while (t--) {
    long long int n, a, b;
    cin >> n >> a >> b;
    long long int e;
    if (n % 2 == 0) {
      e = n / 2 - 1;
    } else {
      e = n / 2;
    }
    if (a > e || b > e || a + b > n - 2 || abs(b - a) > 1) {
      cout << -1 << "\n";
    } else {
      int v[n];
      if (a == b) {
        for (int i = 0; i <= n - 1; i++) {
          v[i] = i + 1;
        }
      } else if (a > b) {
        v[n - 1] = 1;
        for (int i = 0; i <= n - 2; i++) {
          v[i] = i + 2;
        }
        a--;
      } else {
        v[0] = n;
        for (int i = 1; i <= n - 1; i++) {
          v[i] = i;
        }
      }
      int i = 1;
      if (b > a) {
        i = 2;
      }
      while (a--) {
        swap(v[i], v[i + 1]);
        i += 2;
      }
      for (int i = 0; i <= n - 1; i++) {
        cout << v[i] << " ";
      }
      cout << "\n";
    }
  }
  return 0;
}

### Prompt

In Cpp, your task is to solve 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() {
  const unsigned int M = 1000000007;
  long long int t;
  cin >> t;
  while (t--) {
    long long int n, a, b;
    cin >> n >> a >> b;
    long long int e;
    if (n % 2 == 0) {
      e = n / 2 - 1;
    } else {
      e = n / 2;
    }
    if (a > e || b > e || a + b > n - 2 || abs(b - a) > 1) {
      cout << -1 << "\n";
    } else {
      int v[n];
      if (a == b) {
        for (int i = 0; i <= n - 1; i++) {
          v[i] = i + 1;
        }
      } else if (a > b) {
        v[n - 1] = 1;
        for (int i = 0; i <= n - 2; i++) {
          v[i] = i + 2;
        }
        a--;
      } else {
        v[0] = n;
        for (int i = 1; i <= n - 1; i++) {
          v[i] = i;
        }
      }
      int i = 1;
      if (b > a) {
        i = 2;
      }
      while (a--) {
        swap(v[i], v[i + 1]);
        i += 2;
      }
      for (int i = 0; i <= n - 1; i++) {
        cout << v[i] << " ";
      }
      cout << "\n";
    }
  }
  return 0;
}

```