#include <bits/stdc++.h>
using namespace std;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
const long long int INF = 1e9 + 9;
void fast() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
}
void solve() {
  long long tt = 1;
  cin >> tt;
  while (tt--) {
    long long n, a, b;
    cin >> n >> a >> b;
    vector<long long> ans;
    for (int i = 0; i < n; ++i) {
      ans.push_back(i + 1);
    }
    if ((a + b) > n - 2 || abs(a - b) > 1) {
      cout << -1 << "\n";
    } else {
      if (a == b) {
        for (long long i = 1, j = 1; j <= a; j++, i += 2)
          swap(ans[i], ans[i + 1]);
      }
      if (a > b) {
        for (long long i = n - 1, j = 1; j <= a; j++, i -= 2)
          swap(ans[i], ans[i - 1]);
      }
      if (a < b) {
        for (long long i = 0, j = 1; j <= b; j++, i += 2)
          swap(ans[i], ans[i + 1]);
      }
      for (long long i = 0; i < n; i++) {
        cout << ans[i] << " ";
      }
    }
    cout << "\n";
  }
}
int main() {
  fast();
  solve();
}

### Prompt

Please formulate 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;
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
const long long int INF = 1e9 + 9;
void fast() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
}
void solve() {
  long long tt = 1;
  cin >> tt;
  while (tt--) {
    long long n, a, b;
    cin >> n >> a >> b;
    vector<long long> ans;
    for (int i = 0; i < n; ++i) {
      ans.push_back(i + 1);
    }
    if ((a + b) > n - 2 || abs(a - b) > 1) {
      cout << -1 << "\n";
    } else {
      if (a == b) {
        for (long long i = 1, j = 1; j <= a; j++, i += 2)
          swap(ans[i], ans[i + 1]);
      }
      if (a > b) {
        for (long long i = n - 1, j = 1; j <= a; j++, i -= 2)
          swap(ans[i], ans[i - 1]);
      }
      if (a < b) {
        for (long long i = 0, j = 1; j <= b; j++, i += 2)
          swap(ans[i], ans[i + 1]);
      }
      for (long long i = 0; i < n; i++) {
        cout << ans[i] << " ";
      }
    }
    cout << "\n";
  }
}
int main() {
  fast();
  solve();
}

```