#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization("unroll-loops")
using namespace std;
const long double Pi = 3.141592653;
const long long mod = 998244353;
long long INF = 1000000000000000000;
struct mycmp {
  bool operator()(pair<int, int> a, pair<int, int> b) const {
    return (a.first < b.first) || (a.first == b.first && a.second > b.second);
  }
};
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  cin >> t;
  while (t--) {
    long long n, a, b;
    cin >> n >> a >> b;
    set<int> s;
    for (int i = 1; i <= n; i++) s.insert(i);
    vector<long long> arr(n + 1, 0);
    int diff = abs(a - b);
    int p = max(a, b);
    if (diff > 1 || p > (n - 1) / 2)
      cout << -1 << "\n";
    else if (a == 0 && b == 0) {
      for (int i = 1; i <= n; i++) cout << i << " ";
      cout << "\n";
    } else if (diff == 0) {
      int y = 1;
      for (int i = 2; i <= n; i = i + 2) {
        arr[i] = y;
        ++y;
      }
      int p = n;
      for (int i = 1; i <= n; i = i + 2) {
        arr[i] = p;
        --p;
      }
      for (int i = 2; i < n; i++) {
        if (arr[i] > arr[i - 1] && arr[i] > arr[i + 1]) {
          --a;
        }
        if (arr[i] < arr[i - 1] && arr[i] < arr[i + 1]) {
          --b;
        }
        if (a == 0 && b == 0) {
          sort(arr.begin() + i + 1, arr.end());
          reverse(arr.begin() + 1 + i, arr.end());
          break;
        }
      }
      if (a || b)
        cout << -1 << "\n";
      else {
        for (long long i = 1; i <= n; i++) cout << arr[i] << " ";
        cout << "\n";
      }
    } else if (a > b) {
      int y = n;
      for (int i = 2; i <= n; i = i + 2) {
        arr[i] = y;
        --y;
      }
      int p = 1;
      for (int i = 1; i <= n; i = i + 2) {
        arr[i] = p;
        ++p;
      }
      for (int i = 2; i < n; i++) {
        if (arr[i] > arr[i - 1] && arr[i] > arr[i + 1]) {
          --a;
        }
        if (arr[i] < arr[i - 1] && arr[i] < arr[i + 1]) {
          --b;
        }
        if (a == 0 && b == 0) {
          sort(arr.begin() + i, arr.end());
          reverse(arr.begin() + i, arr.end());
          break;
        }
      }
      for (long long i = 1; i <= n; i++) cout << arr[i] << " ";
      cout << "\n";
    } else {
      int y = 1;
      for (int i = 2; i <= n; i = i + 2) {
        arr[i] = y;
        ++y;
      }
      int p = n;
      for (int i = 1; i <= n; i = i + 2) {
        arr[i] = p;
        --p;
      }
      for (int i = 2; i < n; i++) {
        if (arr[i] > arr[i - 1] && arr[i] > arr[i + 1]) {
          --a;
        }
        if (arr[i] < arr[i - 1] && arr[i] < arr[i + 1]) {
          --b;
        }
        if (a == 0 && b == 0) {
          sort(arr.begin() + i, arr.end());
          break;
        }
      }
      for (long long i = 1; i <= n; i++) cout << arr[i] << " ";
      cout << "\n";
    }
  }
}

### Prompt

Your task is to create 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>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization("unroll-loops")
using namespace std;
const long double Pi = 3.141592653;
const long long mod = 998244353;
long long INF = 1000000000000000000;
struct mycmp {
  bool operator()(pair<int, int> a, pair<int, int> b) const {
    return (a.first < b.first) || (a.first == b.first && a.second > b.second);
  }
};
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  cin >> t;
  while (t--) {
    long long n, a, b;
    cin >> n >> a >> b;
    set<int> s;
    for (int i = 1; i <= n; i++) s.insert(i);
    vector<long long> arr(n + 1, 0);
    int diff = abs(a - b);
    int p = max(a, b);
    if (diff > 1 || p > (n - 1) / 2)
      cout << -1 << "\n";
    else if (a == 0 && b == 0) {
      for (int i = 1; i <= n; i++) cout << i << " ";
      cout << "\n";
    } else if (diff == 0) {
      int y = 1;
      for (int i = 2; i <= n; i = i + 2) {
        arr[i] = y;
        ++y;
      }
      int p = n;
      for (int i = 1; i <= n; i = i + 2) {
        arr[i] = p;
        --p;
      }
      for (int i = 2; i < n; i++) {
        if (arr[i] > arr[i - 1] && arr[i] > arr[i + 1]) {
          --a;
        }
        if (arr[i] < arr[i - 1] && arr[i] < arr[i + 1]) {
          --b;
        }
        if (a == 0 && b == 0) {
          sort(arr.begin() + i + 1, arr.end());
          reverse(arr.begin() + 1 + i, arr.end());
          break;
        }
      }
      if (a || b)
        cout << -1 << "\n";
      else {
        for (long long i = 1; i <= n; i++) cout << arr[i] << " ";
        cout << "\n";
      }
    } else if (a > b) {
      int y = n;
      for (int i = 2; i <= n; i = i + 2) {
        arr[i] = y;
        --y;
      }
      int p = 1;
      for (int i = 1; i <= n; i = i + 2) {
        arr[i] = p;
        ++p;
      }
      for (int i = 2; i < n; i++) {
        if (arr[i] > arr[i - 1] && arr[i] > arr[i + 1]) {
          --a;
        }
        if (arr[i] < arr[i - 1] && arr[i] < arr[i + 1]) {
          --b;
        }
        if (a == 0 && b == 0) {
          sort(arr.begin() + i, arr.end());
          reverse(arr.begin() + i, arr.end());
          break;
        }
      }
      for (long long i = 1; i <= n; i++) cout << arr[i] << " ";
      cout << "\n";
    } else {
      int y = 1;
      for (int i = 2; i <= n; i = i + 2) {
        arr[i] = y;
        ++y;
      }
      int p = n;
      for (int i = 1; i <= n; i = i + 2) {
        arr[i] = p;
        --p;
      }
      for (int i = 2; i < n; i++) {
        if (arr[i] > arr[i - 1] && arr[i] > arr[i + 1]) {
          --a;
        }
        if (arr[i] < arr[i - 1] && arr[i] < arr[i + 1]) {
          --b;
        }
        if (a == 0 && b == 0) {
          sort(arr.begin() + i, arr.end());
          break;
        }
      }
      for (long long i = 1; i <= n; i++) cout << arr[i] << " ";
      cout << "\n";
    }
  }
}

```