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.":
assistant
#Here is Python code to find any such permutation.
 def find(n, a, b):
    if abs(a - b) > 1:
        return -1
    if a + b > n-2:
        return -1
    up = [n-i for i in range(a)]
    down = [i+1 for i in range(b)]
    combine = [str(b+1), ]
    if a == b:
        for i in range(a):
            combine.append(str(up[i]))
            combine.append(str(down[i]))
    else:
        c = b
        if a < b:
            up, down = down, up
            c = a
        for i in range(c):
            combine.append(str(up[i]))
            combine.append(str(down[i]))
        combine.append(str(up[-1]))
    if int(combine[-1]) == n-a+1:
        for i in range(n-a, b+1, -1):
            combine.append(str(i))
    else:
        for i in range(b + 2, n - a + 1):
            combine.append(str(i))
    return ' '.join(combine)

cases = int(input())
for y in range(cases):
    line = input().split( )
    n, a, b = int(line[0]), int(line[1]), int(line[2])
    print(find(n, a, b))