human
Write me a Python program to find any such permutation given the following:
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.
Using python3 can you solve the prior task?
assistant
#Here is Python program to find any such permutation.

for _ in range(int(input())):
    def main():
        n, a, b = map(int, input().split())
        if abs(a-b) > 1:
            return print(-1)
        nums = []
        if a > b:
            if n < a*2+1:
                return print(-1)
            nums.append(1)
            for i in range(n, a*2+1, -1):
                nums.append(i)
            for i in range(a):
                nums.append(a*2+1-i)
                nums.append(i+2)
        elif a == b:
            if n < a*2+2:
                return print(-1)
            for i in range(n, a*2+2, -1):
                nums.append(i)
            for i in range(a+1):
                nums.append(a*2+2-i)
                nums.append(i+1)
        else:
            if n < b*2+1:
                return print(-1)
            for i in range(n, b*2, -1):
                nums.append(i)
            for i in range(b):
                nums.append(i+1)
                nums.append(b*2-i)
        print(' '.join(map(str, nums)))

    main()