human
PYTHON3 solution for "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.":


 Give me a Python program to find any such permutation?
assistant
#Here is Python program to find any such permutation.
 def main():
    n, local_max, local_min = list(map(int, input().split()))

    if abs(local_max - local_min) > 1:
        return [-1]
    if local_max + local_min > n - 2:
        return [-1]
    arr = [0] * n

    if local_max == local_min:
        i = 2
        cur_num = 1
        while local_min > 0:
            arr[i] = cur_num
            i += 2
            local_min -= 1
            cur_num += 1
        for j in range(n):
            if arr[j] == 0:
                arr[j] = cur_num
                cur_num += 1
    elif local_max > local_min:
        i = 1
        cur_num = n
        while local_max > 0:
            arr[i] = cur_num
            i += 2
            local_max -= 1
            cur_num -= 1
        for j in range(n):
            if arr[j] == 0:
                arr[j] = cur_num
                cur_num -= 1
    elif local_min > local_max:
        i = 1
        cur_num = 1
        while local_min > 0:
            arr[i] = cur_num
            i += 2
            local_min -= 1
            cur_num += 1
        for j in range(n):
            if arr[j] == 0:
                arr[j] = cur_num
                cur_num += 1

    # print(arr)
    return arr

for _ in range(int(input())):
    a = main()
    print(*a)