#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int t;
  cin >> t;
  while (t--) {
    long long int n, a, b;
    cin >> n >> a >> b;
    long long int copy = (n - 2);
    long long int Max = ceil(((n - 2) * 1.0) / 2);
    if (a == 0 && b == 0) {
      copy = n;
      for (int i = 0; i < n; i++) {
        cout << copy << " ";
        copy--;
      }
      cout << "\n";
      continue;
    }
    if ((a > Max || b > Max) || (a + b) > n - 2) {
      cout << -1 << endl;
      continue;
    }
    if ((a == 0 && b != 1) || (b == 0 && a != 1)) {
      cout << -1 << endl;
      continue;
    }
    if (abs(a - b) > 1) {
      cout << -1 << endl;
      continue;
    }
    copy = n;
    long long int copy1 = 1, k = 0, l = 0;
    vector<long long int> ans;
    if (a > b) {
      for (int i = 0; i < n; i++) {
        if (k == a) {
          break;
        }
        if (i % 2 == 0) {
          ans.push_back(copy1);
          copy1++;
        } else {
          if (i >= 1 && i < n - 1) {
            k++;
          }
          ans.push_back(copy);
          copy--;
        }
      }
      if (ans.size() == n) {
        for (int i = 0; i < n; i++) {
          cout << ans[i] << " ";
        }
        cout << "\n";
      } else {
        for (int i = ans.size(); i < n; i++) {
          ans.push_back(copy);
          copy--;
        }
        for (int i = 0; i < n; i++) {
          cout << ans[i] << " ";
        }
        cout << "\n";
      }
    } else if (b > a) {
      for (int i = 0; i < n; i++) {
        if (k == b) {
          break;
        }
        if (i % 2 == 0) {
          ans.push_back(copy);
          copy--;
        } else {
          if (i >= 1 && i < n - 1) {
            k++;
          }
          ans.push_back(copy1);
          copy1++;
        }
      }
      if (ans.size() == n) {
        for (int i = 0; i < n; i++) {
          cout << ans[i] << " ";
        }
        cout << "\n";
      } else {
        for (int i = ans.size(); i < n; i++) {
          ans.push_back(copy1);
          copy1++;
        }
        for (int i = 0; i < n; i++) {
          cout << ans[i] << " ";
        }
        cout << "\n";
      }
    } else {
      for (int i = 0; i < n; i++) {
        if (k == a && l == b) {
          break;
        }
        if (i % 2 == 0) {
          if (i >= 2 && i <= n - 2) {
            l++;
          }
          ans.push_back(copy1);
          copy1++;
        } else {
          if (i >= 1 && i < n - 1) {
            k++;
          }
          ans.push_back(copy);
          copy--;
        }
      }
      if (ans.size() == n) {
        for (int i = 0; i < n; i++) {
          cout << ans[i] << " ";
        }
        cout << "\n";
      } else {
        for (int i = ans.size(); i < n; i++) {
          ans.push_back(copy1);
          copy1++;
        }
        for (int i = 0; i < n; i++) {
          cout << ans[i] << " ";
        }
        cout << "\n";
      }
    }
  }
}

### Prompt

Generate a CPP solution 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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int t;
  cin >> t;
  while (t--) {
    long long int n, a, b;
    cin >> n >> a >> b;
    long long int copy = (n - 2);
    long long int Max = ceil(((n - 2) * 1.0) / 2);
    if (a == 0 && b == 0) {
      copy = n;
      for (int i = 0; i < n; i++) {
        cout << copy << " ";
        copy--;
      }
      cout << "\n";
      continue;
    }
    if ((a > Max || b > Max) || (a + b) > n - 2) {
      cout << -1 << endl;
      continue;
    }
    if ((a == 0 && b != 1) || (b == 0 && a != 1)) {
      cout << -1 << endl;
      continue;
    }
    if (abs(a - b) > 1) {
      cout << -1 << endl;
      continue;
    }
    copy = n;
    long long int copy1 = 1, k = 0, l = 0;
    vector<long long int> ans;
    if (a > b) {
      for (int i = 0; i < n; i++) {
        if (k == a) {
          break;
        }
        if (i % 2 == 0) {
          ans.push_back(copy1);
          copy1++;
        } else {
          if (i >= 1 && i < n - 1) {
            k++;
          }
          ans.push_back(copy);
          copy--;
        }
      }
      if (ans.size() == n) {
        for (int i = 0; i < n; i++) {
          cout << ans[i] << " ";
        }
        cout << "\n";
      } else {
        for (int i = ans.size(); i < n; i++) {
          ans.push_back(copy);
          copy--;
        }
        for (int i = 0; i < n; i++) {
          cout << ans[i] << " ";
        }
        cout << "\n";
      }
    } else if (b > a) {
      for (int i = 0; i < n; i++) {
        if (k == b) {
          break;
        }
        if (i % 2 == 0) {
          ans.push_back(copy);
          copy--;
        } else {
          if (i >= 1 && i < n - 1) {
            k++;
          }
          ans.push_back(copy1);
          copy1++;
        }
      }
      if (ans.size() == n) {
        for (int i = 0; i < n; i++) {
          cout << ans[i] << " ";
        }
        cout << "\n";
      } else {
        for (int i = ans.size(); i < n; i++) {
          ans.push_back(copy1);
          copy1++;
        }
        for (int i = 0; i < n; i++) {
          cout << ans[i] << " ";
        }
        cout << "\n";
      }
    } else {
      for (int i = 0; i < n; i++) {
        if (k == a && l == b) {
          break;
        }
        if (i % 2 == 0) {
          if (i >= 2 && i <= n - 2) {
            l++;
          }
          ans.push_back(copy1);
          copy1++;
        } else {
          if (i >= 1 && i < n - 1) {
            k++;
          }
          ans.push_back(copy);
          copy--;
        }
      }
      if (ans.size() == n) {
        for (int i = 0; i < n; i++) {
          cout << ans[i] << " ";
        }
        cout << "\n";
      } else {
        for (int i = ans.size(); i < n; i++) {
          ans.push_back(copy1);
          copy1++;
        }
        for (int i = 0; i < n; i++) {
          cout << ans[i] << " ";
        }
        cout << "\n";
      }
    }
  }
}

```