#V. XHXMMMl317hKWg#+`@@

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n

传统题

2000ms

256MiB

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Statement

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.

Format

Input

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 $10^5$ .

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.

Sample

3
7
4 6 11 11 15 18 20
4
10 10 10 11
3
1 1 1000000000

2 3 6
-1
1 2 3

ShanghaiTech ACM 炸鱼杯

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状态: 已结束
规则: OI
题目: 46
开始于: 2024-12-10 23:00
结束于: 2024-12-15 13:00
持续时间: 110 小时
主持人: _Arahc_
参赛人数: 112

#V. XHXMMMl317hKWg#+`@@

XHXMMMl317hKWg#+`@@

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ShanghaiTech ACM 炸鱼杯

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#V. XHXMMMl317hKWg#+`@@

XHXMMMl317hKWg#+`@@

Statement

Format

Input

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Sample

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