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 program to find any such permutation.
 def solve():
    n, a, b = map(int, input().split())
    ans = [-1] * n
    if abs(a - b) > 1:
        print(-1)
        return
    if a + b + 2 > n:
        print(-1)
        return
    if a == b:
        ans[a + b + 1:] = [i for i in range(a + b + 2, n + 1)]
        smallest = [i for i in range(1, a + b + 2)]
        l, r = 0, len(smallest) - 1
        for i in range(a + b + 1):
            if i % 2 == 0:
                ans[i] = smallest[l]
                l += 1
            else:
                ans[i] = smallest[r]
                r -= 1
    elif a == b + 1:
        largest = [i for i in range(n - (a + b + 1), n + 1)]
        l, r = 0, len(largest) - 1
        ans[:n - (a + b + 2)] = [i for i in range(1, n - (a + b + 1))]
        for i in range(n - (a + b + 2), n):
            if i % 2 == (n - (a + b + 2)) % 2:
                ans[i] = largest[l]
                l += 1
            else:
                ans[i] = largest[r]
                r -= 1
    else:
        ans[:n - (a + b + 2)] = [i for i in range(n, a + b + 2, -1)]
        smallest = [i for i in range(1, a + b + 3)]
        l, r = 0, len(smallest) - 1
        for i in range(n - (a + b + 2), n):
            if i % 2 == (n - (a + b + 2)) % 2:
                ans[i] = smallest[r]
                r -= 1
            else:
                ans[i] = smallest[l]
                l += 1

    print(*ans)

for _ in range(int(input())):
    solve()