CF1398A 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.

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.