Antares's classroom has $$$k$$$ seats that lie uniformly on a circle, labelled $$$1, 2, \dots, k$$$ in clockwise order.
In a particular class, he has $$$n$$$ students, each sitting in one of the $$$k$$$ seats. Each student occupies exactly one seat, and no two students share the same seat. Antares has an array $$$a$$$ of length $$$n$$$, which serves as a seating chart for the class, where student $$$i$$$ is sitting in the seat labelled $$$a_i$$$ for each $$$i=1,2,\dots,n$$$.
Antares recently realized that his students only talk to classmates sitting close to them. This is not good! Because of this, he wants to encourage students to talk to classmates who sit far away.
To do this, he wants to pick a pair of students such that the distance between the two students he picks is the greatest among the distances between any pair of two students.
The distance between two students is the minimum number of seats one needs to pass to reach the other, walking clockwise or counter-clockwise around the circle, including the destination seat (but not including the starting seat).
Please help Antares find two such students.
The first line 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 $$$k$$$ $$$(2 \le n \le 10^5, n \le k \le 10^9)$$$ — the number of students in the class and the number of seats in the class, respectively.
The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ $$$(1 \le a_i \le k)$$$, indicating student $$$i$$$ is sitting in the seat labelled $$$a_i$$$. All values of $$$a_i$$$ are distinct.
It is guaranteed that the sum of $$$n$$$ across all test cases does not exceed $$$2 \cdot 10^5$$$.
For each test case, output two integers $$$i$$$ and $$$j$$$, indicating Antares should pick students $$$i$$$ and $$$j$$$. If there are multiple answers, output any of them.
4 4 7 7 3 5 2 3 8 1 6 3 2 2 1 2 5 10000 1 10 100 1000 10000
3 4 2 1 1 2 5 4
Let $$$d(x,y)$$$ denote the distance between students $$$x$$$ and $$$y$$$.
For the first test case, we have the following classroom:
We have $$$d(1,2)=3$$$, $$$d(1,3)=2$$$, $$$d(1,4)=2$$$, $$$d(2,3)=2$$$, $$$d(2,4)=1$$$, $$$d(3,4)=3$$$. Since the largest distance is $$$3$$$, Antares can pick students $$$3$$$ and $$$4$$$. For this test case, 1 2 is also acceptable.
