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.":


 ... Can you provide a Python program to find any such permutation?
assistant
#Here is Python program to find any such permutation.
 def buildPermutation(n,a,b):
    array = [x for x in range(1,n+1)]
    if abs(a-b) >1:
        return [-1]
    if a==b:
        if (n-2)//2 < a:
            return [-1]
        for x in range(a):
            array[2*(x+1)-1],array[(2*(x+1))] = array[(2*(x+1))],array[2*(x+1)-1]
        return array



    else:
        if (n-3)//2 < min(a,b):
            return [-1]
        if a > b:
            array[0],array[1] = array[1],array[0]
            a-=1
            for x in range(a):
                array[2 * (x + 1)], array[(2 * (x + 1)) + 1] = array[(2 * (x + 1)) + 1], array[2 * (x + 1)]
        else:
            array[-1],array[-2] = array[-2],array[-1]
            b-=1

            for x in range(b):
                array[2*(x+1)-1],array[(2*(x+1))] = array[(2*(x+1))],array[2*(x+1)-1]

        return array


t = int(input())
for _ in range(t):
    n,a,b = map(int,input().split())
    ans = buildPermutation(n,b,a)
    for x in ans:
        print(x,end=" ")
    print()