#D5851. Bad Triangle
Bad Triangle
Bad Triangle
You are given an array a_1, a_2, ... , a_n, which is sorted in non-decreasing order (a_i ≤ a_{i + 1}).
Find three indices i, j, k such that 1 ≤ i < j < k ≤ n and it is impossible to construct a non-degenerate triangle (a triangle with nonzero area) having sides equal to a_i, a_j and a_k (for example it is possible to construct a non-degenerate triangle with sides 3, 4 and 5 but impossible with sides 3, 4 and 7). If it is impossible to find such triple, report it.
Input
The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.
The first line of each test case contains one integer n (3 ≤ n ≤ 5 ⋅ 10^4) — the length of the array a.
The second line of each test case contains n integers a_1, a_2, ... , a_n (1 ≤ a_i ≤ 10^9; a_{i - 1} ≤ a_i) — the array a.
It is guaranteed that the sum of n over all test cases does not exceed 10^5.
Output
For each test case print the answer to it in one line.
If there is a triple of indices i, j, k (i < j < k) such that it is impossible to construct a non-degenerate triangle having sides equal to a_i, a_j and a_k, print that three indices in ascending order. If there are multiple answers, print any of them.
Otherwise, print -1.
Example
Input
3 7 4 6 11 11 15 18 20 4 10 10 10 11 3 1 1 1000000000
Output
2 3 6 -1 1 2 3
Note
In the first test case it is impossible with sides 6, 11 and 18. Note, that this is not the only correct answer.
In the second test case you always can construct a non-degenerate triangle.
inputFormat
Input
The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.
The first line of each test case contains one integer n (3 ≤ n ≤ 5 ⋅ 10^4) — the length of the array a.
The second line of each test case contains n integers a_1, a_2, ... , a_n (1 ≤ a_i ≤ 10^9; a_{i - 1} ≤ a_i) — the array a.
It is guaranteed that the sum of n over all test cases does not exceed 10^5.
outputFormat
Output
For each test case print the answer to it in one line.
If there is a triple of indices i, j, k (i < j < k) such that it is impossible to construct a non-degenerate triangle having sides equal to a_i, a_j and a_k, print that three indices in ascending order. If there are multiple answers, print any of them.
Otherwise, print -1.
Example
Input
3 7 4 6 11 11 15 18 20 4 10 10 10 11 3 1 1 1000000000
Output
2 3 6 -1 1 2 3
Note
In the first test case it is impossible with sides 6, 11 and 18. Note, that this is not the only correct answer.
In the second test case you always can construct a non-degenerate triangle.
样例
3
7
4 6 11 11 15 18 20
4
10 10 10 11
3
1 1 1000000000
1 2 7
-1
1 2 3