human
Can you solve the below in PYTHON3?
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 code to find any such permutation?
assistant
#Here is Python code to find any such permutation.

# def condition(mid, n, arr):
#     count = 0
#     for i in range(1, n):
#         if arr[i] - arr[i - 1] > mid:
#             count += mid
#         else:
#             count += arr[i] - arr[i - 1]
#     count += mid
#     return count

# for _ in range(int(input())):
#     n, h = list(map(int, input().split()))
# array = list(map(int, input().split()))
#     hig = h - 1
#     low = 1
#     while low <= hig:
#         mid = low + (hig - low) // 2
#         if condition(mid, n, array) > h:
#             hig = mid - 1
#         else:
#             low = mid + 1
#     print(low, hig)
# # n, h = 5, 3
# # array = [1, 2, 4, 5, 7]
# # hig = h - 1
# # low = array[0]
# # while low < hig:
# #     mid = low + (hig - low) // 2
# #     if condition(mid, n, array) > h:
# #         hig = mid - 1
# #     else:
# #         low = mid + 1
# # print(low)

# for _ in range(int(input())):
#     n = int(input())
#     string = input()
#     s = ["aa", "aba", "aca", "abca", "acba", "abbacca", "accabba"]
#     for i in s:
#         if i in string:
#             print(len(i))
#             break
#     else:
#         print(-1)

# for _ in range(int(input())):
#     n = int(input())
# array = list(map(int, input().split()))
#     if n % 2 == 0:
#         print("YES")
#     else:
#         for i in range(1, n):
#             if array[i - 1] >= array[i]:
#                 print("YES")
#                 break
#         else:
#             print("NO")
# def condition(mid, main_arr):
#     for i in range(len(main_arr)):
#         if mid > main_arr[i][0]:
#             mid += main_arr[i][1]
#         else:
#             return False
#     return True

# for _ in range(int(input())):
#     n = int(input())
#     main_arr = []
#     minn = float("inf")
#     for _ in range(n):
#         arr = list(map(int, input().split()))
#         n = arr[0]
#         arr = [] + arr[1:]
#         maxx = max(arr)
#         maxx_index = arr.index(maxx)
#         main_arr.append([maxx - maxx_index + 1, n])

#     main_arr.sort()
#     lo = main_arr[0][0]
#...