A. Bad Triangle
geometry; math
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.
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.