#include <bits/stdc++.h>
using namespace std;
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return (a / gcd(a, b) * b); }
bool sorta(const pair<int, int>& a, const pair<int, int>& b) {
  return (a.second < b.second);
}
bool sortd(const pair<int, int>& a, const pair<int, int>& b) {
  return (a.second > b.second);
}
void printarr(long long arr[], long long n) {
  for (int i = 0; i < n; i++) cout << arr[i] << " ";
  cout << "\n";
}
string decToBinary(int n) {
  string s = "";
  int i = 0;
  while (n > 0) {
    s = to_string(n % 2) + s;
    n = n / 2;
    i++;
  }
  return s;
}
long long binaryToDecimal(string n) {
  string num = n;
  long long dec_value = 0;
  int base = 1;
  int len = num.length();
  for (int i = len - 1; i >= 0; i--) {
    if (num[i] == '1') dec_value += base;
    base = base * 2;
  }
  return dec_value;
}
bool isPrime(int n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (int i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
bool isPowerOfTwo(int n) {
  if (n == 0) return false;
  return (ceil(log2(n)) == floor(log2(n)));
}
bool checksame(int a[], int n) {
  for (int i = 1; i < n; i++) {
    if (a[i] != a[i - 1]) return false;
  }
  return true;
}
int fact(int n) { return (n == 1 || n == 0) ? 1 : n * fact(n - 1); }
long long mod = 1e9 + 7;
bool cmp(pair<int, int>& a, pair<int, int>& b) { return a.second > b.second; }
vector<pair<int, int>> sort(map<int, int>& M) {
  vector<pair<int, int>> A;
  for (auto& it : M) {
    A.push_back(it);
  }
  sort(A.begin(), A.end(), cmp);
  return A;
}
void BHAI() {
  long long n, a, b;
  cin >> n >> a >> b;
  if (a + b > n - 2)
    cout << "-1\n";
  else if (abs(a - b) > 1)
    cout << "-1\n";
  else {
    if (a == 0 && b == 0) {
      for (int i = 0; i < n; i++) cout << i + 1 << " ";
      cout << "\n";
    } else if (a == 1 && b == 0) {
      for (int i = 1; i <= n - 2; i++) cout << i << " ";
      cout << n << " " << n - 1 << "\n";
    } else if (a == 0 && b == 1) {
      cout << "2 1"
           << " ";
      for (int i = 3; i <= n; i++) cout << i << " ";
      cout << "\n";
    } else {
      long long x;
      if (a > b) {
        x = a + b + 1;
        for (int i = 1; i <= n - x; i++) cout << i << " ";
        for (int i = n - x + 1; i <= n; i += 2) {
          cout << i + 1 << " " << i << " ";
        }
        cout << "\n";
      } else if (b > a) {
        x = a + b + 1;
        for (int i = 1; i <= x; i += 2) {
          cout << i + 1 << " " << i << " ";
        }
        for (int i = x + 1; i <= n; i++) {
          cout << i << " ";
        }
        cout << "\n";
      } else {
        x = a + b;
        for (int i = 1; i <= x; i += 2) {
          cout << i + 1 << " " << i << " ";
        }
        for (int i = x + 1; i <= n - 2; i++) {
          cout << i << " ";
        }
        cout << n << " " << n - 1 << " ";
        cout << "\n";
      }
    }
  }
}
int main() {
  long long t;
  cin >> t;
  while (t--) {
    BHAI();
  }
  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;
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return (a / gcd(a, b) * b); }
bool sorta(const pair<int, int>& a, const pair<int, int>& b) {
  return (a.second < b.second);
}
bool sortd(const pair<int, int>& a, const pair<int, int>& b) {
  return (a.second > b.second);
}
void printarr(long long arr[], long long n) {
  for (int i = 0; i < n; i++) cout << arr[i] << " ";
  cout << "\n";
}
string decToBinary(int n) {
  string s = "";
  int i = 0;
  while (n > 0) {
    s = to_string(n % 2) + s;
    n = n / 2;
    i++;
  }
  return s;
}
long long binaryToDecimal(string n) {
  string num = n;
  long long dec_value = 0;
  int base = 1;
  int len = num.length();
  for (int i = len - 1; i >= 0; i--) {
    if (num[i] == '1') dec_value += base;
    base = base * 2;
  }
  return dec_value;
}
bool isPrime(int n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  for (int i = 5; i * i <= n; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}
bool isPowerOfTwo(int n) {
  if (n == 0) return false;
  return (ceil(log2(n)) == floor(log2(n)));
}
bool checksame(int a[], int n) {
  for (int i = 1; i < n; i++) {
    if (a[i] != a[i - 1]) return false;
  }
  return true;
}
int fact(int n) { return (n == 1 || n == 0) ? 1 : n * fact(n - 1); }
long long mod = 1e9 + 7;
bool cmp(pair<int, int>& a, pair<int, int>& b) { return a.second > b.second; }
vector<pair<int, int>> sort(map<int, int>& M) {
  vector<pair<int, int>> A;
  for (auto& it : M) {
    A.push_back(it);
  }
  sort(A.begin(), A.end(), cmp);
  return A;
}
void BHAI() {
  long long n, a, b;
  cin >> n >> a >> b;
  if (a + b > n - 2)
    cout << "-1\n";
  else if (abs(a - b) > 1)
    cout << "-1\n";
  else {
    if (a == 0 && b == 0) {
      for (int i = 0; i < n; i++) cout << i + 1 << " ";
      cout << "\n";
    } else if (a == 1 && b == 0) {
      for (int i = 1; i <= n - 2; i++) cout << i << " ";
      cout << n << " " << n - 1 << "\n";
    } else if (a == 0 && b == 1) {
      cout << "2 1"
           << " ";
      for (int i = 3; i <= n; i++) cout << i << " ";
      cout << "\n";
    } else {
      long long x;
      if (a > b) {
        x = a + b + 1;
        for (int i = 1; i <= n - x; i++) cout << i << " ";
        for (int i = n - x + 1; i <= n; i += 2) {
          cout << i + 1 << " " << i << " ";
        }
        cout << "\n";
      } else if (b > a) {
        x = a + b + 1;
        for (int i = 1; i <= x; i += 2) {
          cout << i + 1 << " " << i << " ";
        }
        for (int i = x + 1; i <= n; i++) {
          cout << i << " ";
        }
        cout << "\n";
      } else {
        x = a + b;
        for (int i = 1; i <= x; i += 2) {
          cout << i + 1 << " " << i << " ";
        }
        for (int i = x + 1; i <= n - 2; i++) {
          cout << i << " ";
        }
        cout << n << " " << n - 1 << " ";
        cout << "\n";
      }
    }
  }
}
int main() {
  long long t;
  cin >> t;
  while (t--) {
    BHAI();
  }
  return 0;
}

```