You are given an array $$$a$$$ of length $$$n$$$ and an integer $$$m$$$. Find three distinct indices $$$1 \le i, j, k \le n$$$ such that $$$m \le a_i + a_j + a_k \le 2m$$$, or report that no such indices exist.
Each test consists of multiple test cases.
The first line of input contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.
The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$3 \le n \le 2 \cdot 10^5$$$, $$$1 \le m \le 3 \cdot 10^8$$$) — the length of the array $$$a$$$ and the target sum, respectively.
The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^8$$$) — the array $$$a$$$ as described above.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
For each test case, if there is no solution, print a single integer $$$-1$$$.
Otherwise, print three distinct integers $$$i$$$, $$$j$$$, $$$k$$$ ($$$1 \le i, j, k \le n$$$) such that $$$m \le a_i + a_j + a_k \le 2m$$$.
If there are multiple solutions, you may print any.
45 101 4 6 9 25 201 4 6 9 23 13 4 510 225 1 2 9 3 1 1 3 10 6
2 3 4 -1 -1 8 9 4
In the first test case, we have $$$a_2 + a_3 + a_4 = 19$$$, which is in the range $$$[10, 20]$$$.
In the second test case, it can be shown that no triple satisfies the condition $$$20 \le a_i + a_j + a_k \le 40$$$.
