#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 10;
int x[N];
int t;
int n, a, b;
int main() {
  scanf("%d", &t);
  while (t--) {
    scanf("%d%d%d", &n, &a, &b);
    if (a + b + 2 > n) {
      printf("-1\n");
      continue;
    }
    if (a > b + 1 || b > a + 1) {
      printf("-1\n");
      continue;
    }
    for (int i = 1; i <= n; i++) {
      x[i] = i;
    }
    if (a == b) {
      for (int i = 2; a; i += 2) {
        swap(x[i], x[i + 1]);
        a--;
      }
    } else if (a > b) {
      swap(x[n - 1], x[n]);
      for (int i = 2; b; i += 2) {
        swap(x[i], x[i + 1]);
        b--;
      }
    } else {
      swap(x[1], x[2]);
      for (int i = 3; a; i += 2) {
        swap(x[i], x[i + 1]);
        a--;
      }
    }
    for (int i = 1; i <= n; i++) {
      printf("%d ", x[i]);
    }
    printf("\n");
  }
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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 = 2e5 + 10;
int x[N];
int t;
int n, a, b;
int main() {
  scanf("%d", &t);
  while (t--) {
    scanf("%d%d%d", &n, &a, &b);
    if (a + b + 2 > n) {
      printf("-1\n");
      continue;
    }
    if (a > b + 1 || b > a + 1) {
      printf("-1\n");
      continue;
    }
    for (int i = 1; i <= n; i++) {
      x[i] = i;
    }
    if (a == b) {
      for (int i = 2; a; i += 2) {
        swap(x[i], x[i + 1]);
        a--;
      }
    } else if (a > b) {
      swap(x[n - 1], x[n]);
      for (int i = 2; b; i += 2) {
        swap(x[i], x[i + 1]);
        b--;
      }
    } else {
      swap(x[1], x[2]);
      for (int i = 3; a; i += 2) {
        swap(x[i], x[i + 1]);
        a--;
      }
    }
    for (int i = 1; i <= n; i++) {
      printf("%d ", x[i]);
    }
    printf("\n");
  }
  return 0;
}

```