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.":


 ... Write me a Python program to find any such permutation?
assistant
#Here is Python program to find any such permutation.
 def swaps(arr,i,a):
    n = len(arr)
    while(i+1<n):
        arr[i],arr[i+1]=arr[i+1],arr[i]
        a-=1
        if(a==0):
            break
        i+=2
    return arr
for i in range(int(input())):
    n,a,b = list(map(int, input().split()))
    arr = [i for i in range(1,n+1)]
    done=0
    if(a==0 and b==0):
        print(*arr)
        done=1
    elif(abs(a-b)>1 or a+b>n-2):
        print(-1)
        done=1
    elif(max(a,b)>(n//2+n%2)):
        print(-1)
        done=0
    if(done==0):
        if(a>b):
            arr.reverse()
            arr = swaps(arr,0,a)
        elif(a<b):
            arr = swaps(arr,0,b)
        else:
            arr = swaps(arr,1,b)
        print(*arr)