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 rev(a,l,r):
    while(l<r):
        a[l],a[r]=a[r],a[l]
        l+=1
        r-=1
for _ in range(int(input())):
    n,a,b=map(int,input().split())
    if(abs(a-b)>1 or (a+b)>n-2):
        print(-1)
        continue
    arr=[i+1 for i in range(n)]
    if(a==0 and b==0):
        print(*arr)
        continue
    if(a==0):
        rev(arr,0,n-1)
        rev(arr,1,n-1)
        print(*arr)
        continue
    if(b==0):
        rev(arr,1,n-1)
        print(*arr)
        continue
    if(a>b):
        i=n-1
        cnt=a
        while(cnt):
            arr[i],arr[i-1]=arr[i-1],arr[i]
            i-=2
            cnt-=1
        print(*arr)
        continue
    if(b>a):
        i=0
        cnt=b
        while(cnt):
            arr[i],arr[i+1]=arr[i+1],arr[i]
            i+=2
            cnt-=1
        print(*arr)
        continue
    if(a==b):
        i=1
        cnt=a
        while(cnt):
            arr[i],arr[i+1]=arr[i+1],arr[i]
            i+=2
            cnt-=1
        print(*arr)
        continue