A13746 | Bad Triangle

You are given an array $a_1, a_2, \dots , a_n$ , which is sorted in non-decreasing order ( $a_i \le a_{i + 1})$ .

Find three indices $i$ , $j$ , $k$ such that $1 \le i < j < k \le n$ 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.

The first line contains one integer $t$ ( $1 \le t \le 1000$ ) — the number of test cases.

The first line of each test case contains one integer $n$ ( $3 \le n \le 5 \cdot 10^4$ ) — the length of the array $a$ .

The second line of each test case contains $n$ integers $a_1, a_2, \dots , a_n$ ( $1 \le a_i \le 10^9$ ; $a_{i - 1} \le a_i$ ) — the array $a$ .

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$ .

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.