#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 100;
int z[N], ans[N];
int n, m;
int main() {
  int t;
  cin >> t;
  while (t--) {
    int a, b, f = 0;
    cin >> n >> a >> b;
    if (a == b) f = 1;
    if (abs(a - b) > 1 || a + b > n - 2) {
      cout << -1 << endl;
      continue;
    } else if (a >= b)
      for (int i = 1; i <= n; i++) z[i] = i;
    else
      for (int i = 1; i <= n; i++) z[i] = n - i + 1;
    ans[1] = z[1];
    int i = 2, j = n, k = 2, sum = a + b;
    for (int p = 1; p <= sum; k++, p++) {
      if (p & 1)
        ans[k] = z[j--], b--;
      else
        ans[k] = z[i++], a--;
    }
    if (f)
      while (k <= n) ans[k++] = z[i++];
    else
      while (k <= n) ans[k++] = z[j--];
    for (int p = 1; p <= n; p++) cout << ans[p] << ' ';
    cout << endl;
  }
}

### 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;
const int N = 1e5 + 100;
int z[N], ans[N];
int n, m;
int main() {
  int t;
  cin >> t;
  while (t--) {
    int a, b, f = 0;
    cin >> n >> a >> b;
    if (a == b) f = 1;
    if (abs(a - b) > 1 || a + b > n - 2) {
      cout << -1 << endl;
      continue;
    } else if (a >= b)
      for (int i = 1; i <= n; i++) z[i] = i;
    else
      for (int i = 1; i <= n; i++) z[i] = n - i + 1;
    ans[1] = z[1];
    int i = 2, j = n, k = 2, sum = a + b;
    for (int p = 1; p <= sum; k++, p++) {
      if (p & 1)
        ans[k] = z[j--], b--;
      else
        ans[k] = z[i++], a--;
    }
    if (f)
      while (k <= n) ans[k++] = z[i++];
    else
      while (k <= n) ans[k++] = z[j--];
    for (int p = 1; p <= n; p++) cout << ans[p] << ' ';
    cout << endl;
  }
}

```